Well I don’t know if the Consistency-check would be Computationally-feasible, because of course there are a lot of ways to divide a large electorate into 2 parts. That might be one more good reason to use Approval instead, for those single-winner elections. On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff <email9648742@gmail.com> wrote: > I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & propose it > for Germany’s single-winner elections, including the single member district > elections in their Additional-Member proportional topping-up Parliamentary > elections. > > On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff <email9648742@gmail.com> > wrote: > >> >> >> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >> closed.limelike.curves@gmail.com> wrote: >> >>> . Some alternative criterion that gets us "99% of the way to Condorcet," >>>> so it behaves like Condorcet except in the rare cases where it conflicts >>>> with participation (or maybe just mono-add-top/remove-bottom). >>> >>> >> There might be better ways, but there’s always the lexicographical way. >> The criterion could require that Participation (& other >> non-opposite-response criteria) & Consistency be met. …& that the voted >> CW, when there is one must be elected when that doesn’t conflict with the >> above requirements. >> >> A complying method could just repeat that wording, along with a >> specification about what to do if there’s no voted CW, & what to do if the >> ballot-configuration is such that additional of a new ballot could violate >> Participation, or if some division of the electorate into 2 parts could >> show a Consistency violation. >> >> Maybe apply Implicit-Approval to the ballots then. (Ranked = approved) >> >>> >>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>> closed.limelike.curves@gmail.com> wrote: >>> >>>> It’s surprising that participation-violation is unconstitutional in >>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>> >>>> I'm actually not sure it is--the Supreme Court has never ruled on , and >>>> courts also haven't ruled on the constitutionality of non-monotone voting >>>> rules. STV has been upheld as constitutional in the past, but the >>>> challenges were never brought over monotonicity failures. It's entirely >>>> possible a new challenge could overturn it; there's a strong argument that >>>> monotonicity failures violate due process and the equal protection clause. >>>> >>>> The ideal case to bring to the Supreme Court would have been for >>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>> Court, without being too controversial. Being the Condorcet winner makes >>>> his case look even stronger. >>>> >>>> On the other hand, if someone says the word "monotonicity" in front of >>>> a judge, their eyes will glaze over and they'll immediately stop >>>> caring about all this weird, complicated nerd math. The way to explain >>>> participation failures is to run a ton of ads explaining to Alaska >>>> Republicans that Begich lost because *he got* *too many votes. * >>>> >>>> One suggestion: why not rename monotonicity to "helpfulness?" (Voting >>>> should help your candidate, not hurt them). We can call monotonicity >>>> failures "spitefulness" (because the system is going out of its way to do >>>> the opposite of what you ask it to). >>>> >>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>> email9648742@gmail.com> wrote: >>>> >>>>> It’s surprising that participation-violation is unconstitutional in >>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>> >>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet isn’t. >>>>> Nonmonotonicity is just defined to give Condorcet, with it’s >>>>> participation-failure, a pass. >>>>> >>>>> I’ve heard that Participation & the Condorcet Criterion are mutually >>>>> incompatible. I feel that participation-failure is an acceptable price for >>>>> the Condorcet Criterion. Always electing the voted CW brings strategy >>>>> improvement, & the unpredictable & rare participation-failure is probably >>>>> irrelevant to strategy. >>>>> >>>>> But that incompatibility, along with the ones Arrow pointed-out, shows >>>>> that single-winner elections aren’t perfect. …making a good argument for >>>>> PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>> >>>>> Maybe, as a PR country (like 2/3 of the world’s countries), Germany >>>>> feels no need to compromise participation. >>>>> >>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of the >>>>> world’s countries for about a century. >>>>> >>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re stuck >>>>> in the 18th century, & always will be, while most of the world has moved on >>>>> to democracy. >>>>> >>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>> closed.limelike.curves@gmail.com> wrote: >>>>> >>>>>> Can Condorcet be weakened to comply with participation? Condorcet >>>>>> methods have plenty of advantages, but systems failing participation are >>>>>> vulnerable to court challenges or being struck down as unconstitutional, as >>>>>> seen in Germany. >>>>>> ---- >>>>>> Election-Methods mailing list - see https://electorama.com/em for >>>>>> list info >>>>>> >>>>>

Maybe it might be good enough to just require that there must not be a Participation-violation with respect to any one of the voters, had s/he voted last? On Wed, Feb 28, 2024 at 22:17 Michael Ossipoff <email9648742@gmail.com> wrote: > Well I don’t know if the Consistency-check would be > Computationally-feasible, because of course there are a lot of ways to > divide a large electorate into 2 parts. > > That might be one more good reason to use Approval instead, for those > single-winner elections. > > On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff <email9648742@gmail.com> > wrote: > >> I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & propose it >> for Germany’s single-winner elections, including the single member district >> elections in their Additional-Member proportional topping-up Parliamentary >> elections. >> >> On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff <email9648742@gmail.com> >> wrote: >> >>> >>> >>> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >>> closed.limelike.curves@gmail.com> wrote: >>> >>>> . Some alternative criterion that gets us "99% of the way to >>>>> Condorcet," so it behaves like Condorcet except in the rare cases where it >>>>> conflicts with participation (or maybe just mono-add-top/remove-bottom). >>>> >>>> >>> There might be better ways, but there’s always the lexicographical way. >>> The criterion could require that Participation (& other >>> non-opposite-response criteria) & Consistency be met. …& that the voted >>> CW, when there is one must be elected when that doesn’t conflict with the >>> above requirements. >>> >>> A complying method could just repeat that wording, along with a >>> specification about what to do if there’s no voted CW, & what to do if the >>> ballot-configuration is such that additional of a new ballot could violate >>> Participation, or if some division of the electorate into 2 parts could >>> show a Consistency violation. >>> >>> Maybe apply Implicit-Approval to the ballots then. (Ranked = approved) >>> >>>> >>>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>>> closed.limelike.curves@gmail.com> wrote: >>>> >>>>> It’s surprising that participation-violation is unconstitutional in >>>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>> >>>>> I'm actually not sure it is--the Supreme Court has never ruled on , >>>>> and courts also haven't ruled on the constitutionality of non-monotone >>>>> voting rules. STV has been upheld as constitutional in the past, but the >>>>> challenges were never brought over monotonicity failures. It's entirely >>>>> possible a new challenge could overturn it; there's a strong argument that >>>>> monotonicity failures violate due process and the equal protection clause. >>>>> >>>>> The ideal case to bring to the Supreme Court would have been for >>>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>>> Court, without being too controversial. Being the Condorcet winner makes >>>>> his case look even stronger. >>>>> >>>>> On the other hand, if someone says the word "monotonicity" in front of >>>>> a judge, their eyes will glaze over and they'll immediately stop >>>>> caring about all this weird, complicated nerd math. The way to explain >>>>> participation failures is to run a ton of ads explaining to Alaska >>>>> Republicans that Begich lost because *he got* *too many votes. * >>>>> >>>>> One suggestion: why not rename monotonicity to "helpfulness?" (Voting >>>>> should help your candidate, not hurt them). We can call monotonicity >>>>> failures "spitefulness" (because the system is going out of its way to do >>>>> the opposite of what you ask it to). >>>>> >>>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>>> email9648742@gmail.com> wrote: >>>>> >>>>>> It’s surprising that participation-violation is unconstitutional in >>>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>> >>>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet isn’t. >>>>>> Nonmonotonicity is just defined to give Condorcet, with it’s >>>>>> participation-failure, a pass. >>>>>> >>>>>> I’ve heard that Participation & the Condorcet Criterion are mutually >>>>>> incompatible. I feel that participation-failure is an acceptable price for >>>>>> the Condorcet Criterion. Always electing the voted CW brings strategy >>>>>> improvement, & the unpredictable & rare participation-failure is probably >>>>>> irrelevant to strategy. >>>>>> >>>>>> But that incompatibility, along with the ones Arrow pointed-out, >>>>>> shows that single-winner elections aren’t perfect. …making a good argument >>>>>> for PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>>> >>>>>> Maybe, as a PR country (like 2/3 of the world’s countries), Germany >>>>>> feels no need to compromise participation. >>>>>> >>>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of the >>>>>> world’s countries for about a century. >>>>>> >>>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re stuck >>>>>> in the 18th century, & always will be, while most of the world has moved on >>>>>> to democracy. >>>>>> >>>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>> >>>>>>> Can Condorcet be weakened to comply with participation? Condorcet >>>>>>> methods have plenty of advantages, but systems failing participation are >>>>>>> vulnerable to court challenges or being struck down as unconstitutional, as >>>>>>> seen in Germany. >>>>>>> ---- >>>>>>> Election-Methods mailing list - see https://electorama.com/em for >>>>>>> list info >>>>>>> >>>>>>

That seems to exclude participation failures except in the case of near-ties; I think adding a batch of ballots, all of which rank A>B, shouldn't cause B to defeat A. I don't think we need perfect consistency, just participation. Consistency failures are paradoxical, but consistency is a very strong criterion and isn't needed for the weaker case of participation (which limits consistency to the ). It's also strong enough that it could lock you into Kemeny-Young (the unique order-consistent Condorcet method). Checking for participation naively definitely isn't feasible, so we'd need a more elegant approach. Alternatively, we could try finding a Condorcet system that violates participation "as little as possible," in the sense that any participation failures are forced by Condorcet-compliance. A judge might be willing to sign off on that, since it's a tradeoff between two similarly-important values (equal protection and majority rule). On Wed, Feb 28, 2024 at 10:30 PM Michael Ossipoff <email9648742@gmail.com> wrote: > Maybe it might be good enough to just require that there must not be a > Participation-violation with respect to any one of the voters, had s/he > voted last? > > On Wed, Feb 28, 2024 at 22:17 Michael Ossipoff <email9648742@gmail.com> > wrote: > >> Well I don’t know if the Consistency-check would be >> Computationally-feasible, because of course there are a lot of ways to >> divide a large electorate into 2 parts. >> >> That might be one more good reason to use Approval instead, for those >> single-winner elections. >> >> On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff <email9648742@gmail.com> >> wrote: >> >>> I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & propose >>> it for Germany’s single-winner elections, including the single member >>> district elections in their Additional-Member proportional topping-up >>> Parliamentary elections. >>> >>> On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff <email9648742@gmail.com> >>> wrote: >>> >>>> >>>> >>>> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >>>> closed.limelike.curves@gmail.com> wrote: >>>> >>>>> . Some alternative criterion that gets us "99% of the way to >>>>>> Condorcet," so it behaves like Condorcet except in the rare cases where it >>>>>> conflicts with participation (or maybe just mono-add-top/remove-bottom). >>>>> >>>>> >>>> There might be better ways, but there’s always the lexicographical way. >>>> The criterion could require that Participation (& other >>>> non-opposite-response criteria) & Consistency be met. …& that the voted >>>> CW, when there is one must be elected when that doesn’t conflict with the >>>> above requirements. >>>> >>>> A complying method could just repeat that wording, along with a >>>> specification about what to do if there’s no voted CW, & what to do if the >>>> ballot-configuration is such that additional of a new ballot could violate >>>> Participation, or if some division of the electorate into 2 parts could >>>> show a Consistency violation. >>>> >>>> Maybe apply Implicit-Approval to the ballots then. (Ranked = approved) >>>> >>>>> >>>>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>>>> closed.limelike.curves@gmail.com> wrote: >>>>> >>>>>> It’s surprising that participation-violation is unconstitutional in >>>>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>> >>>>>> I'm actually not sure it is--the Supreme Court has never ruled on , >>>>>> and courts also haven't ruled on the constitutionality of non-monotone >>>>>> voting rules. STV has been upheld as constitutional in the past, but the >>>>>> challenges were never brought over monotonicity failures. It's entirely >>>>>> possible a new challenge could overturn it; there's a strong argument that >>>>>> monotonicity failures violate due process and the equal protection clause. >>>>>> >>>>>> The ideal case to bring to the Supreme Court would have been for >>>>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>>>> Court, without being too controversial. Being the Condorcet winner makes >>>>>> his case look even stronger. >>>>>> >>>>>> On the other hand, if someone says the word "monotonicity" in front >>>>>> of a judge, their eyes will glaze over and they'll immediately stop >>>>>> caring about all this weird, complicated nerd math. The way to explain >>>>>> participation failures is to run a ton of ads explaining to Alaska >>>>>> Republicans that Begich lost because *he got* *too many votes. * >>>>>> >>>>>> One suggestion: why not rename monotonicity to "helpfulness?" (Voting >>>>>> should help your candidate, not hurt them). We can call monotonicity >>>>>> failures "spitefulness" (because the system is going out of its way to do >>>>>> the opposite of what you ask it to). >>>>>> >>>>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>>>> email9648742@gmail.com> wrote: >>>>>> >>>>>>> It’s surprising that participation-violation is unconstitutional in >>>>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>> >>>>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet >>>>>>> isn’t. Nonmonotonicity is just defined to give Condorcet, with it’s >>>>>>> participation-failure, a pass. >>>>>>> >>>>>>> I’ve heard that Participation & the Condorcet Criterion are mutually >>>>>>> incompatible. I feel that participation-failure is an acceptable price for >>>>>>> the Condorcet Criterion. Always electing the voted CW brings strategy >>>>>>> improvement, & the unpredictable & rare participation-failure is probably >>>>>>> irrelevant to strategy. >>>>>>> >>>>>>> But that incompatibility, along with the ones Arrow pointed-out, >>>>>>> shows that single-winner elections aren’t perfect. …making a good argument >>>>>>> for PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>>>> >>>>>>> Maybe, as a PR country (like 2/3 of the world’s countries), Germany >>>>>>> feels no need to compromise participation. >>>>>>> >>>>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of the >>>>>>> world’s countries for about a century. >>>>>>> >>>>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re >>>>>>> stuck in the 18th century, & always will be, while most of the world has >>>>>>> moved on to democracy. >>>>>>> >>>>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>> >>>>>>>> Can Condorcet be weakened to comply with participation? Condorcet >>>>>>>> methods have plenty of advantages, but systems failing participation are >>>>>>>> vulnerable to court challenges or being struck down as unconstitutional, as >>>>>>>> seen in Germany. >>>>>>>> ---- >>>>>>>> Election-Methods mailing list - see https://electorama.com/em for >>>>>>>> list info >>>>>>>> >>>>>>>

On 2024-02-28 19:36, Closed Limelike Curves wrote: > Can Condorcet be weakened to comply with participation? Condorcet > methods have plenty of advantages, but systems failing participation are > vulnerable to court challenges or being struck down as unconstitutional, > as seen in Germany. In the mathematical sense, there exists some voting method that maximizes the probability that when a random election is chosen, according to some election distribution, and that election has a CW, then that CW is elected -- while still respecting participation. In that sense, Condorcet can be weakened and such a method is the method that weakens it the least. But what it actually looks like, or what its algorithm would be like, nobody knows. You could get a glimpse into how it behaves for low numbers of voters and candidates by using a variant of my integer programming approach, but it doesn't tell you much: it basically amounts to a gigantic lookup table. In general, determining the minimal relaxations of some criterion required to pass some other criterion is very hard. I can really only think of two examples: Schulze STV's resistance to vote management except when it would conflict with Droop proportionality, and the independence of strongly dominated alternatives criterion of River as a monotone approximation to independence of covered alternatives. And I don't think Jobst set out to make a method to be close to IoCA while passing monotonicity, so Schulze's the only example I can think of where the designer set out to find a relaxation of that sort. -km

Yes, I too feel that though Consistency-failure is an embarrassment, it’s Participation-failure—where a particular voter should have stayed home—that is the rights-violation. Yes, maybe there’s some big subset of the voters, say 37%, such that, if they’d stayed home the result of applying the method to the other 63% (which would then have been the actual election-result) would have been the same as the result of applying it to them separately…but, because they voted, a different result happened. That doesn’t sound as bad as Participation-failure. 1. That 37%’s hypothetical collective-choice by the method isn’t as definite & stark as a person’s expressed-preference. 2. A *different outcome* from the hypothetical result of applying the method to the 37% isn’t as concretely clearly wrong as outright negative-response to someone’s expressed preference. …& that’s a good thing, because checking for Consistency-failure is what DOES sound computationally infeasible due to the many ways of dividing a large electorate into 2 par. Checking for Participation-failure would just be a matter of, for each voter, doing the count without hir ballot & determining whether that changes the winner to someone s/he ranked above the actual winner. With 300,000,000 voters that isn’t infeasible with today’s computers is it? I should have asked: In Germany, is Consistency-failure unconstitutional? That might be a problem for Condorcet. If only Participation-failure is unconstitutional, then wouldn’t Kobe computationally-feasible to check for that? When a Participation-failure is found, then elect the winner by Implicit-Approval. In wv, not ranking candidates you don’t like is good defensive-strategy anyway. If it’s known that many people vote that way, wv’s already good burial-deterrence is further enhanced. On Thu, Feb 29, 2024 at 10:06 Closed Limelike Curves < closed.limelike.curves@gmail.com> wrote: > That seems to exclude participation failures except in the case > of near-ties; I think adding a batch of ballots, all of which rank A>B, > shouldn't cause B to defeat A. > > I don't think we need perfect consistency, just participation. Consistency > failures are paradoxical, but consistency is a very strong criterion and > isn't needed for the weaker case of participation (which limits consistency > to the ). It's also strong enough that it could lock you into Kemeny-Young > (the unique order-consistent Condorcet method). > > Checking for participation naively definitely isn't feasible, so we'd need > a more elegant approach. > > Alternatively, we could try finding a Condorcet system that violates > participation "as little as possible," in the sense that any participation > failures are forced by Condorcet-compliance. A judge might be willing to > sign off on that, since it's a tradeoff between two similarly-important > values (equal protection and majority rule). > > On Wed, Feb 28, 2024 at 10:30 PM Michael Ossipoff <email9648742@gmail.com> > wrote: > >> Maybe it might be good enough to just require that there must not be a >> Participation-violation with respect to any one of the voters, had s/he >> voted last? >> >> On Wed, Feb 28, 2024 at 22:17 Michael Ossipoff <email9648742@gmail.com> >> wrote: >> >>> Well I don’t know if the Consistency-check would be >>> Computationally-feasible, because of course there are a lot of ways to >>> divide a large electorate into 2 parts. >>> >>> That might be one more good reason to use Approval instead, for those >>> single-winner elections. >>> >>> On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff <email9648742@gmail.com> >>> wrote: >>> >>>> I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & propose >>>> it for Germany’s single-winner elections, including the single member >>>> district elections in their Additional-Member proportional topping-up >>>> Parliamentary elections. >>>> >>>> On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff <email9648742@gmail.com> >>>> wrote: >>>> >>>>> >>>>> >>>>> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >>>>> closed.limelike.curves@gmail.com> wrote: >>>>> >>>>>> . Some alternative criterion that gets us "99% of the way to >>>>>>> Condorcet," so it behaves like Condorcet except in the rare cases where it >>>>>>> conflicts with participation (or maybe just mono-add-top/remove-bottom). >>>>>> >>>>>> >>>>> There might be better ways, but there’s always the lexicographical >>>>> way. The criterion could require that Participation (& other >>>>> non-opposite-response criteria) & Consistency be met. …& that the voted >>>>> CW, when there is one must be elected when that doesn’t conflict with the >>>>> above requirements. >>>>> >>>>> A complying method could just repeat that wording, along with a >>>>> specification about what to do if there’s no voted CW, & what to do if the >>>>> ballot-configuration is such that additional of a new ballot could violate >>>>> Participation, or if some division of the electorate into 2 parts could >>>>> show a Consistency violation. >>>>> >>>>> Maybe apply Implicit-Approval to the ballots then. (Ranked = approved) >>>>> >>>>>> >>>>>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>> >>>>>>> It’s surprising that participation-violation is unconstitutional in >>>>>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>> >>>>>>> I'm actually not sure it is--the Supreme Court has never ruled on , >>>>>>> and courts also haven't ruled on the constitutionality of non-monotone >>>>>>> voting rules. STV has been upheld as constitutional in the past, but the >>>>>>> challenges were never brought over monotonicity failures. It's entirely >>>>>>> possible a new challenge could overturn it; there's a strong argument that >>>>>>> monotonicity failures violate due process and the equal protection clause. >>>>>>> >>>>>>> The ideal case to bring to the Supreme Court would have been for >>>>>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>>>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>>>>> Court, without being too controversial. Being the Condorcet winner makes >>>>>>> his case look even stronger. >>>>>>> >>>>>>> On the other hand, if someone says the word "monotonicity" in front >>>>>>> of a judge, their eyes will glaze over and they'll immediately stop >>>>>>> caring about all this weird, complicated nerd math. The way to explain >>>>>>> participation failures is to run a ton of ads explaining to Alaska >>>>>>> Republicans that Begich lost because *he got* *too many votes. * >>>>>>> >>>>>>> One suggestion: why not rename monotonicity to "helpfulness?" >>>>>>> (Voting should help your candidate, not hurt them). We can call >>>>>>> monotonicity failures "spitefulness" (because the system is going out of >>>>>>> its way to do the opposite of what you ask it to). >>>>>>> >>>>>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>>>>> email9648742@gmail.com> wrote: >>>>>>> >>>>>>>> It’s surprising that participation-violation is unconstitutional in >>>>>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>> >>>>>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet >>>>>>>> isn’t. Nonmonotonicity is just defined to give Condorcet, with it’s >>>>>>>> participation-failure, a pass. >>>>>>>> >>>>>>>> I’ve heard that Participation & the Condorcet Criterion are >>>>>>>> mutually incompatible. I feel that participation-failure is an acceptable >>>>>>>> price for the Condorcet Criterion. Always electing the voted CW brings >>>>>>>> strategy improvement, & the unpredictable & rare participation-failure is >>>>>>>> probably irrelevant to strategy. >>>>>>>> >>>>>>>> But that incompatibility, along with the ones Arrow pointed-out, >>>>>>>> shows that single-winner elections aren’t perfect. …making a good argument >>>>>>>> for PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>>>>> >>>>>>>> Maybe, as a PR country (like 2/3 of the world’s countries), Germany >>>>>>>> feels no need to compromise participation. >>>>>>>> >>>>>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of the >>>>>>>> world’s countries for about a century. >>>>>>>> >>>>>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re >>>>>>>> stuck in the 18th century, & always will be, while most of the world has >>>>>>>> moved on to democracy. >>>>>>>> >>>>>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>> >>>>>>>>> Can Condorcet be weakened to comply with participation? Condorcet >>>>>>>>> methods have plenty of advantages, but systems failing participation are >>>>>>>>> vulnerable to court challenges or being struck down as unconstitutional, as >>>>>>>>> seen in Germany. >>>>>>>>> ---- >>>>>>>>> Election-Methods mailing list - see https://electorama.com/em for >>>>>>>>> list info >>>>>>>>> >>>>>>>>

It should be noted that the world's most widely used, most frequently used voting method is Condorcet-consistent, and therefore doesn't satisfy Participation.  I'm referring to the Robert's Rules "sequential pairwise" method for voting on motions.  If a court gives this due consideration, they would be unreasonable and arbitrary to be overly concerned about Participation.  Other criteria are much more important.  It's a reasonable bet that the decision by the court in Germany was corrupted by the desire to maintain the basic properties of their existing system, which favors the existing political elite, not the voters' best interests. The Participation criterion compares the winner given sincere voting to the winner given abstention.  That's a false dichotomy.  When a voter has the information needed to deduce that abstention (nonparticipation) is probably a better strategy than sincere voting, that same information leads to a participating voting strategy at least as good as abstention.  Surely such strategies would be widely publicized when needed to defeat an extremist or loathed "greater evil."  Also, given a good Condorcetian voting method (such as Maximize Affirmed Majorities). typically the different winner would not be an extremist greater evil, so the change of winner shouldn't matter much.  The reason that would be typical is that a good Condorcetian voting method creates a strong incentive for candidates who want to win to support policies preferred by majorities. (Median-ish policies.)  A small change of votes would typically cause only a small change of the resultant policies, unlike with other voting methods (including proportional representation), where participation is much more important.  Creating that incentive for candidates & parties is what I consider the most important criterion for voting methods -- it would lead to the end of political polarization, stabilize policies, reduce the incentive for vote fraud & voter suppression, etc -- but unfortunately it's hard to formally define it. If earlier replies have already mentioned some of the above points, sorry about that.  I don't have enough spare time to read all the other replies. --S On 2/28/2024 1:36 PM, Closed Limelike Curves wrote: > Can Condorcet be weakened to comply with participation? Condorcet methods have plenty of advantages, but systems failing participation are vulnerable to court challenges or being struck down as unconstitutional, as seen in Germany.

Ahh, I see what you mean–we can check for participation failures by checking the result with ballots[1:i] and comparing with ballots[1:(i+1)]. I misunderstood you as saying we could compare ballots and ballots[Not(i)]. Couldn't this new procedure still violate participation? What if adding ballots[i] with A>B would cause B>A, but B also happens to win under implicit approval voting? On Thu, Feb 29, 2024 at 4:02 PM Michael Ossipoff <email9648742@gmail.com> wrote: > Yes, I too feel that though Consistency-failure is an embarrassment, it’s > Participation-failure—where a particular voter should have stayed home—that > is the rights-violation. > > Yes, maybe there’s some big subset of the voters, say 37%, such that, if > they’d stayed home the result of applying the method to the other 63% > (which would then have been the actual election-result) would have been the > same as the result of applying it to them separately…but, because they > voted, a different result happened. > > That doesn’t sound as bad as Participation-failure. > > 1. That 37%’s hypothetical collective-choice by the method isn’t as > definite & stark as a person’s expressed-preference. > > 2. A *different outcome* from the hypothetical result of applying the > method to the 37% isn’t as concretely clearly wrong as outright > negative-response to someone’s expressed preference. > > …& that’s a good thing, because checking for Consistency-failure is what > DOES sound computationally infeasible due to the many ways of dividing a > large electorate into 2 par. > > Checking for Participation-failure would just be a matter of, for each > voter, doing the count without hir ballot & determining whether that > changes the winner to someone s/he ranked above the actual winner. > > With 300,000,000 voters that isn’t infeasible with today’s computers is it? > > I should have asked: > > In Germany, is Consistency-failure unconstitutional? That might be a > problem for Condorcet. If only Participation-failure is unconstitutional, > then wouldn’t Kobe computationally-feasible to check for that? > > When a Participation-failure is found, then elect the winner by > Implicit-Approval. > > In wv, not ranking candidates you don’t like is good defensive-strategy > anyway. If it’s known that many people vote that way, wv’s already good > burial-deterrence is further enhanced. > > > > On Thu, Feb 29, 2024 at 10:06 Closed Limelike Curves < > closed.limelike.curves@gmail.com> wrote: > >> That seems to exclude participation failures except in the case >> of near-ties; I think adding a batch of ballots, all of which rank A>B, >> shouldn't cause B to defeat A. >> >> I don't think we need perfect consistency, just participation. >> Consistency failures are paradoxical, but consistency is a very >> strong criterion and isn't needed for the weaker case of participation >> (which limits consistency to the ). It's also strong enough that it >> could lock you into Kemeny-Young (the unique order-consistent Condorcet >> method). >> >> Checking for participation naively definitely isn't feasible, so we'd >> need a more elegant approach. >> >> Alternatively, we could try finding a Condorcet system that violates >> participation "as little as possible," in the sense that any participation >> failures are forced by Condorcet-compliance. A judge might be willing to >> sign off on that, since it's a tradeoff between two similarly-important >> values (equal protection and majority rule). >> >> On Wed, Feb 28, 2024 at 10:30 PM Michael Ossipoff <email9648742@gmail.com> >> wrote: >> >>> Maybe it might be good enough to just require that there must not be a >>> Participation-violation with respect to any one of the voters, had s/he >>> voted last? >>> >>> On Wed, Feb 28, 2024 at 22:17 Michael Ossipoff <email9648742@gmail.com> >>> wrote: >>> >>>> Well I don’t know if the Consistency-check would be >>>> Computationally-feasible, because of course there are a lot of ways to >>>> divide a large electorate into 2 parts. >>>> >>>> That might be one more good reason to use Approval instead, for those >>>> single-winner elections. >>>> >>>> On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff <email9648742@gmail.com> >>>> wrote: >>>> >>>>> I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & propose >>>>> it for Germany’s single-winner elections, including the single member >>>>> district elections in their Additional-Member proportional topping-up >>>>> Parliamentary elections. >>>>> >>>>> On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff <email9648742@gmail.com> >>>>> wrote: >>>>> >>>>>> >>>>>> >>>>>> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>> >>>>>>> . Some alternative criterion that gets us "99% of the way to >>>>>>>> Condorcet," so it behaves like Condorcet except in the rare cases where it >>>>>>>> conflicts with participation (or maybe just mono-add-top/remove-bottom). >>>>>>> >>>>>>> >>>>>> There might be better ways, but there’s always the lexicographical >>>>>> way. The criterion could require that Participation (& other >>>>>> non-opposite-response criteria) & Consistency be met. …& that the voted >>>>>> CW, when there is one must be elected when that doesn’t conflict with the >>>>>> above requirements. >>>>>> >>>>>> A complying method could just repeat that wording, along with a >>>>>> specification about what to do if there’s no voted CW, & what to do if the >>>>>> ballot-configuration is such that additional of a new ballot could violate >>>>>> Participation, or if some division of the electorate into 2 parts could >>>>>> show a Consistency violation. >>>>>> >>>>>> Maybe apply Implicit-Approval to the ballots then. (Ranked = approved) >>>>>> >>>>>>> >>>>>>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>> >>>>>>>> It’s surprising that participation-violation is unconstitutional in >>>>>>>>> Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>>> >>>>>>>> I'm actually not sure it is--the Supreme Court has never ruled on , >>>>>>>> and courts also haven't ruled on the constitutionality of non-monotone >>>>>>>> voting rules. STV has been upheld as constitutional in the past, but the >>>>>>>> challenges were never brought over monotonicity failures. It's entirely >>>>>>>> possible a new challenge could overturn it; there's a strong argument that >>>>>>>> monotonicity failures violate due process and the equal protection clause. >>>>>>>> >>>>>>>> The ideal case to bring to the Supreme Court would have been for >>>>>>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>>>>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>>>>>> Court, without being too controversial. Being the Condorcet winner makes >>>>>>>> his case look even stronger. >>>>>>>> >>>>>>>> On the other hand, if someone says the word "monotonicity" in front >>>>>>>> of a judge, their eyes will glaze over and they'll immediately stop >>>>>>>> caring about all this weird, complicated nerd math. The way to explain >>>>>>>> participation failures is to run a ton of ads explaining to Alaska >>>>>>>> Republicans that Begich lost because *he got* *too many votes. * >>>>>>>> >>>>>>>> One suggestion: why not rename monotonicity to "helpfulness?" >>>>>>>> (Voting should help your candidate, not hurt them). We can call >>>>>>>> monotonicity failures "spitefulness" (because the system is going out of >>>>>>>> its way to do the opposite of what you ask it to). >>>>>>>> >>>>>>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>>>>>> email9648742@gmail.com> wrote: >>>>>>>> >>>>>>>>> It’s surprising that participation-violation is unconstitutional >>>>>>>>> in Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>>> >>>>>>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet >>>>>>>>> isn’t. Nonmonotonicity is just defined to give Condorcet, with it’s >>>>>>>>> participation-failure, a pass. >>>>>>>>> >>>>>>>>> I’ve heard that Participation & the Condorcet Criterion are >>>>>>>>> mutually incompatible. I feel that participation-failure is an acceptable >>>>>>>>> price for the Condorcet Criterion. Always electing the voted CW brings >>>>>>>>> strategy improvement, & the unpredictable & rare participation-failure is >>>>>>>>> probably irrelevant to strategy. >>>>>>>>> >>>>>>>>> But that incompatibility, along with the ones Arrow pointed-out, >>>>>>>>> shows that single-winner elections aren’t perfect. …making a good argument >>>>>>>>> for PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>>>>>> >>>>>>>>> Maybe, as a PR country (like 2/3 of the world’s countries), >>>>>>>>> Germany feels no need to compromise participation. >>>>>>>>> >>>>>>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of >>>>>>>>> the world’s countries for about a century. >>>>>>>>> >>>>>>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re >>>>>>>>> stuck in the 18th century, & always will be, while most of the world has >>>>>>>>> moved on to democracy. >>>>>>>>> >>>>>>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> Can Condorcet be weakened to comply with participation? Condorcet >>>>>>>>>> methods have plenty of advantages, but systems failing participation are >>>>>>>>>> vulnerable to court challenges or being struck down as unconstitutional, as >>>>>>>>>> seen in Germany. >>>>>>>>>> ---- >>>>>>>>>> Election-Methods mailing list - see https://electorama.com/em >>>>>>>>>> for list info >>>>>>>>>> >>>>>>>>>

Yes, just a matter of, for each voter, decrementing the population-total of every pairwise-preference s/he voted. …& applying RP(wv) to that modified population preference-totals set. But, other than looking at that voter’s ballot, no new votecounting is needed. The entire Participation-check only takes half as long as the original exhaustive pairwise-count used by Condorcet. > Couldn't this new procedure still violate participation? > Not if it’s Implicit-Approval (ranked = approved). What if adding ballots[i] with A>B would cause B>A, but B also happens to > win under implicit approval voting? > That occurred to me too. Well I’d say that the important thing is that after the illegal Participation-failure result is discarded, then even if IA gives the same winner, this time it didn’t happen as a Participation-violation. The discarding makes the election innocent. But Steve is right: For any one of us, the minuscule chance of a preference of ours being negatively responded-to doesn’t even come close to outweighing the strategy-freeness for which RP(wv) is being used. > > > On Thu, Feb 29, 2024 at 4:02 PM Michael Ossipoff <email9648742@gmail.com> > wrote: > >> Yes, I too feel that though Consistency-failure is an embarrassment, it’s >> Participation-failure—where a particular voter should have stayed home—that >> is the rights-violation. >> >> Yes, maybe there’s some big subset of the voters, say 37%, such that, if >> they’d stayed home the result of applying the method to the other 63% >> (which would then have been the actual election-result) would have been the >> same as the result of applying it to them separately…but, because they >> voted, a different result happened. >> >> That doesn’t sound as bad as Participation-failure. >> >> 1. That 37%’s hypothetical collective-choice by the method isn’t as >> definite & stark as a person’s expressed-preference. >> >> 2. A *different outcome* from the hypothetical result of applying the >> method to the 37% isn’t as concretely clearly wrong as outright >> negative-response to someone’s expressed preference. >> >> …& that’s a good thing, because checking for Consistency-failure is what >> DOES sound computationally infeasible due to the many ways of dividing a >> large electorate into 2 par. >> >> Checking for Participation-failure would just be a matter of, for each >> voter, doing the count without hir ballot & determining whether that >> changes the winner to someone s/he ranked above the actual winner. >> >> With 300,000,000 voters that isn’t infeasible with today’s computers is >> it? >> >> I should have asked: >> >> In Germany, is Consistency-failure unconstitutional? That might be a >> problem for Condorcet. If only Participation-failure is unconstitutional, >> then wouldn’t Kobe computationally-feasible to check for that? >> >> When a Participation-failure is found, then elect the winner by >> Implicit-Approval. >> >> In wv, not ranking candidates you don’t like is good defensive-strategy >> anyway. If it’s known that many people vote that way, wv’s already good >> burial-deterrence is further enhanced. >> >> >> >> On Thu, Feb 29, 2024 at 10:06 Closed Limelike Curves < >> closed.limelike.curves@gmail.com> wrote: >> >>> That seems to exclude participation failures except in the case >>> of near-ties; I think adding a batch of ballots, all of which rank A>B, >>> shouldn't cause B to defeat A. >>> >>> I don't think we need perfect consistency, just participation. >>> Consistency failures are paradoxical, but consistency is a very >>> strong criterion and isn't needed for the weaker case of participation >>> (which limits consistency to the ). It's also strong enough that it >>> could lock you into Kemeny-Young (the unique order-consistent Condorcet >>> method). >>> >>> Checking for participation naively definitely isn't feasible, so we'd >>> need a more elegant approach. >>> >>> Alternatively, we could try finding a Condorcet system that violates >>> participation "as little as possible," in the sense that any participation >>> failures are forced by Condorcet-compliance. A judge might be willing >>> to sign off on that, since it's a tradeoff between two similarly-important >>> values (equal protection and majority rule). >>> >>> On Wed, Feb 28, 2024 at 10:30 PM Michael Ossipoff < >>> email9648742@gmail.com> wrote: >>> >>>> Maybe it might be good enough to just require that there must not be a >>>> Participation-violation with respect to any one of the voters, had s/he >>>> voted last? >>>> >>>> On Wed, Feb 28, 2024 at 22:17 Michael Ossipoff <email9648742@gmail.com> >>>> wrote: >>>> >>>>> Well I don’t know if the Consistency-check would be >>>>> Computationally-feasible, because of course there are a lot of ways to >>>>> divide a large electorate into 2 parts. >>>>> >>>>> That might be one more good reason to use Approval instead, for those >>>>> single-winner elections. >>>>> >>>>> On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff <email9648742@gmail.com> >>>>> wrote: >>>>> >>>>>> I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & >>>>>> propose it for Germany’s single-winner elections, including the single >>>>>> member district elections in their Additional-Member proportional >>>>>> topping-up Parliamentary elections. >>>>>> >>>>>> On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff < >>>>>> email9648742@gmail.com> wrote: >>>>>> >>>>>>> >>>>>>> >>>>>>> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>> >>>>>>>> . Some alternative criterion that gets us "99% of the way to >>>>>>>>> Condorcet," so it behaves like Condorcet except in the rare cases where it >>>>>>>>> conflicts with participation (or maybe just mono-add-top/remove-bottom). >>>>>>>> >>>>>>>> >>>>>>> There might be better ways, but there’s always the lexicographical >>>>>>> way. The criterion could require that Participation (& other >>>>>>> non-opposite-response criteria) & Consistency be met. …& that the voted >>>>>>> CW, when there is one must be elected when that doesn’t conflict with the >>>>>>> above requirements. >>>>>>> >>>>>>> A complying method could just repeat that wording, along with a >>>>>>> specification about what to do if there’s no voted CW, & what to do if the >>>>>>> ballot-configuration is such that additional of a new ballot could violate >>>>>>> Participation, or if some division of the electorate into 2 parts could >>>>>>> show a Consistency violation. >>>>>>> >>>>>>> Maybe apply Implicit-Approval to the ballots then. (Ranked = >>>>>>> approved) >>>>>>> >>>>>>>> >>>>>>>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>> >>>>>>>>> It’s surprising that participation-violation is unconstitutional >>>>>>>>>> in Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>>>> >>>>>>>>> I'm actually not sure it is--the Supreme Court has never ruled on >>>>>>>>> , and courts also haven't ruled on the constitutionality of non-monotone >>>>>>>>> voting rules. STV has been upheld as constitutional in the past, but the >>>>>>>>> challenges were never brought over monotonicity failures. It's entirely >>>>>>>>> possible a new challenge could overturn it; there's a strong argument that >>>>>>>>> monotonicity failures violate due process and the equal protection clause. >>>>>>>>> >>>>>>>>> The ideal case to bring to the Supreme Court would have been for >>>>>>>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>>>>>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>>>>>>> Court, without being too controversial. Being the Condorcet winner makes >>>>>>>>> his case look even stronger. >>>>>>>>> >>>>>>>>> On the other hand, if someone says the word "monotonicity" in >>>>>>>>> front of a judge, their eyes will glaze over and they'll immediately stop >>>>>>>>> caring about all this weird, complicated nerd math. The way to explain >>>>>>>>> participation failures is to run a ton of ads explaining to Alaska >>>>>>>>> Republicans that Begich lost because *he got* *too many votes. * >>>>>>>>> >>>>>>>>> One suggestion: why not rename monotonicity to "helpfulness?" >>>>>>>>> (Voting should help your candidate, not hurt them). We can call >>>>>>>>> monotonicity failures "spitefulness" (because the system is going out of >>>>>>>>> its way to do the opposite of what you ask it to). >>>>>>>>> >>>>>>>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>>>>>>> email9648742@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> It’s surprising that participation-violation is unconstitutional >>>>>>>>>> in Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>>>> >>>>>>>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet >>>>>>>>>> isn’t. Nonmonotonicity is just defined to give Condorcet, with it’s >>>>>>>>>> participation-failure, a pass. >>>>>>>>>> >>>>>>>>>> I’ve heard that Participation & the Condorcet Criterion are >>>>>>>>>> mutually incompatible. I feel that participation-failure is an acceptable >>>>>>>>>> price for the Condorcet Criterion. Always electing the voted CW brings >>>>>>>>>> strategy improvement, & the unpredictable & rare participation-failure is >>>>>>>>>> probably irrelevant to strategy. >>>>>>>>>> >>>>>>>>>> But that incompatibility, along with the ones Arrow pointed-out, >>>>>>>>>> shows that single-winner elections aren’t perfect. …making a good argument >>>>>>>>>> for PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>>>>>>> >>>>>>>>>> Maybe, as a PR country (like 2/3 of the world’s countries), >>>>>>>>>> Germany feels no need to compromise participation. >>>>>>>>>> >>>>>>>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of >>>>>>>>>> the world’s countries for about a century. >>>>>>>>>> >>>>>>>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re >>>>>>>>>> stuck in the 18th century, & always will be, while most of the world has >>>>>>>>>> moved on to democracy. >>>>>>>>>> >>>>>>>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> Can Condorcet be weakened to comply with participation? >>>>>>>>>>> Condorcet methods have plenty of advantages, but systems failing >>>>>>>>>>> participation are vulnerable to court challenges or being struck down as >>>>>>>>>>> unconstitutional, as seen in Germany. >>>>>>>>>>> ---- >>>>>>>>>>> Election-Methods mailing list - see https://electorama.com/em >>>>>>>>>>> for list info >>>>>>>>>>> >>>>>>>>>>

> > But Steve is right: For any one of us, the minuscule chance of a > preference of ours being negatively responded-to doesn’t even come close to > outweighing the strategy-freeness for which RP(wv) is being used. > Agree that if RP improves strategy-resistance in practice, a tiny risk of participation failures is worth it. But courts might not agree. More importantly, it means you can't challenge IRV in court on the basis that participation/monotonicity failure violates a fundamental human right (if your own proposed alternative also violates that right). That occurred to me too. Well I’d say that the important thing is that > after the illegal Participation-failure result is discarded, then even if > IA gives the same winner, this time it didn’t happen as a > Participation-violation. > It's still a participation violation--the whole combined electoral system violates participation, even if the specific steps don't. In the same way, there's no individual step of IRV that violates participation (each round is just a plurality vote). It's the process as a whole that does. On Fri, Mar 1, 2024 at 7:49 PM Michael Ossipoff <email9648742@gmail.com> wrote: > Yes, just a matter of, for each voter, decrementing the population-total > of every pairwise-preference s/he voted. …& applying RP(wv) to that > modified population preference-totals set. But, other than looking at that > voter’s ballot, no new votecounting is needed. > > The entire Participation-check only takes half as long as the original > exhaustive pairwise-count used by Condorcet. > > > >> Couldn't this new procedure still violate participation? >> > > Not if it’s Implicit-Approval (ranked = approved). > > > What if adding ballots[i] with A>B would cause B>A, but B also happens to >> win under implicit approval voting? >> > > That occurred to me too. Well I’d say that the important thing is that > after the illegal Participation-failure result is discarded, then even if > IA gives the same winner, this time it didn’t happen as a > Participation-violation. > > The discarding makes the election innocent. > > But Steve is right: For any one of us, the minuscule chance of a > preference of ours being negatively responded-to doesn’t even come close to > outweighing the strategy-freeness for which RP(wv) is being used. > >> >> >> On Thu, Feb 29, 2024 at 4:02 PM Michael Ossipoff <email9648742@gmail.com> >> wrote: >> >>> Yes, I too feel that though Consistency-failure is an embarrassment, >>> it’s Participation-failure—where a particular voter should have stayed >>> home—that is the rights-violation. >>> >>> Yes, maybe there’s some big subset of the voters, say 37%, such that, if >>> they’d stayed home the result of applying the method to the other 63% >>> (which would then have been the actual election-result) would have been the >>> same as the result of applying it to them separately…but, because they >>> voted, a different result happened. >>> >>> That doesn’t sound as bad as Participation-failure. >>> >>> 1. That 37%’s hypothetical collective-choice by the method isn’t as >>> definite & stark as a person’s expressed-preference. >>> >>> 2. A *different outcome* from the hypothetical result of applying the >>> method to the 37% isn’t as concretely clearly wrong as outright >>> negative-response to someone’s expressed preference. >>> >>> …& that’s a good thing, because checking for Consistency-failure is what >>> DOES sound computationally infeasible due to the many ways of dividing a >>> large electorate into 2 par. >>> >>> Checking for Participation-failure would just be a matter of, for each >>> voter, doing the count without hir ballot & determining whether that >>> changes the winner to someone s/he ranked above the actual winner. >>> >>> With 300,000,000 voters that isn’t infeasible with today’s computers is >>> it? >>> >>> I should have asked: >>> >>> In Germany, is Consistency-failure unconstitutional? That might be a >>> problem for Condorcet. If only Participation-failure is unconstitutional, >>> then wouldn’t Kobe computationally-feasible to check for that? >>> >>> When a Participation-failure is found, then elect the winner by >>> Implicit-Approval. >>> >>> In wv, not ranking candidates you don’t like is good defensive-strategy >>> anyway. If it’s known that many people vote that way, wv’s already good >>> burial-deterrence is further enhanced. >>> >>> >>> >>> On Thu, Feb 29, 2024 at 10:06 Closed Limelike Curves < >>> closed.limelike.curves@gmail.com> wrote: >>> >>>> That seems to exclude participation failures except in the case >>>> of near-ties; I think adding a batch of ballots, all of which rank A>B, >>>> shouldn't cause B to defeat A. >>>> >>>> I don't think we need perfect consistency, just participation. >>>> Consistency failures are paradoxical, but consistency is a very >>>> strong criterion and isn't needed for the weaker case of participation >>>> (which limits consistency to the ). It's also strong enough that it >>>> could lock you into Kemeny-Young (the unique order-consistent Condorcet >>>> method). >>>> >>>> Checking for participation naively definitely isn't feasible, so we'd >>>> need a more elegant approach. >>>> >>>> Alternatively, we could try finding a Condorcet system that violates >>>> participation "as little as possible," in the sense that any participation >>>> failures are forced by Condorcet-compliance. A judge might be willing >>>> to sign off on that, since it's a tradeoff between two similarly-important >>>> values (equal protection and majority rule). >>>> >>>> On Wed, Feb 28, 2024 at 10:30 PM Michael Ossipoff < >>>> email9648742@gmail.com> wrote: >>>> >>>>> Maybe it might be good enough to just require that there must not be a >>>>> Participation-violation with respect to any one of the voters, had s/he >>>>> voted last? >>>>> >>>>> On Wed, Feb 28, 2024 at 22:17 Michael Ossipoff <email9648742@gmail.com> >>>>> wrote: >>>>> >>>>>> Well I don’t know if the Consistency-check would be >>>>>> Computationally-feasible, because of course there are a lot of ways to >>>>>> divide a large electorate into 2 parts. >>>>>> >>>>>> That might be one more good reason to use Approval instead, for those >>>>>> single-winner elections. >>>>>> >>>>>> On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff < >>>>>> email9648742@gmail.com> wrote: >>>>>> >>>>>>> I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & >>>>>>> propose it for Germany’s single-winner elections, including the single >>>>>>> member district elections in their Additional-Member proportional >>>>>>> topping-up Parliamentary elections. >>>>>>> >>>>>>> On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff < >>>>>>> email9648742@gmail.com> wrote: >>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>> >>>>>>>>> . Some alternative criterion that gets us "99% of the way to >>>>>>>>>> Condorcet," so it behaves like Condorcet except in the rare cases where it >>>>>>>>>> conflicts with participation (or maybe just mono-add-top/remove-bottom). >>>>>>>>> >>>>>>>>> >>>>>>>> There might be better ways, but there’s always the lexicographical >>>>>>>> way. The criterion could require that Participation (& other >>>>>>>> non-opposite-response criteria) & Consistency be met. …& that the voted >>>>>>>> CW, when there is one must be elected when that doesn’t conflict with the >>>>>>>> above requirements. >>>>>>>> >>>>>>>> A complying method could just repeat that wording, along with a >>>>>>>> specification about what to do if there’s no voted CW, & what to do if the >>>>>>>> ballot-configuration is such that additional of a new ballot could violate >>>>>>>> Participation, or if some division of the electorate into 2 parts could >>>>>>>> show a Consistency violation. >>>>>>>> >>>>>>>> Maybe apply Implicit-Approval to the ballots then. (Ranked = >>>>>>>> approved) >>>>>>>> >>>>>>>>> >>>>>>>>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> It’s surprising that participation-violation is unconstitutional >>>>>>>>>>> in Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>>>>> >>>>>>>>>> I'm actually not sure it is--the Supreme Court has never ruled on >>>>>>>>>> , and courts also haven't ruled on the constitutionality of non-monotone >>>>>>>>>> voting rules. STV has been upheld as constitutional in the past, but the >>>>>>>>>> challenges were never brought over monotonicity failures. It's entirely >>>>>>>>>> possible a new challenge could overturn it; there's a strong argument that >>>>>>>>>> monotonicity failures violate due process and the equal protection clause. >>>>>>>>>> >>>>>>>>>> The ideal case to bring to the Supreme Court would have been for >>>>>>>>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>>>>>>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>>>>>>>> Court, without being too controversial. Being the Condorcet winner makes >>>>>>>>>> his case look even stronger. >>>>>>>>>> >>>>>>>>>> On the other hand, if someone says the word "monotonicity" in >>>>>>>>>> front of a judge, their eyes will glaze over and they'll immediately stop >>>>>>>>>> caring about all this weird, complicated nerd math. The way to explain >>>>>>>>>> participation failures is to run a ton of ads explaining to Alaska >>>>>>>>>> Republicans that Begich lost because *he got* *too many votes. * >>>>>>>>>> >>>>>>>>>> One suggestion: why not rename monotonicity to "helpfulness?" >>>>>>>>>> (Voting should help your candidate, not hurt them). We can call >>>>>>>>>> monotonicity failures "spitefulness" (because the system is going out of >>>>>>>>>> its way to do the opposite of what you ask it to). >>>>>>>>>> >>>>>>>>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>>>>>>>> email9648742@gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> It’s surprising that participation-violation is unconstitutional >>>>>>>>>>> in Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>>>>> >>>>>>>>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet >>>>>>>>>>> isn’t. Nonmonotonicity is just defined to give Condorcet, with it’s >>>>>>>>>>> participation-failure, a pass. >>>>>>>>>>> >>>>>>>>>>> I’ve heard that Participation & the Condorcet Criterion are >>>>>>>>>>> mutually incompatible. I feel that participation-failure is an acceptable >>>>>>>>>>> price for the Condorcet Criterion. Always electing the voted CW brings >>>>>>>>>>> strategy improvement, & the unpredictable & rare participation-failure is >>>>>>>>>>> probably irrelevant to strategy. >>>>>>>>>>> >>>>>>>>>>> But that incompatibility, along with the ones Arrow pointed-out, >>>>>>>>>>> shows that single-winner elections aren’t perfect. …making a good argument >>>>>>>>>>> for PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>>>>>>>> >>>>>>>>>>> Maybe, as a PR country (like 2/3 of the world’s countries), >>>>>>>>>>> Germany feels no need to compromise participation. >>>>>>>>>>> >>>>>>>>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of >>>>>>>>>>> the world’s countries for about a century. >>>>>>>>>>> >>>>>>>>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re >>>>>>>>>>> stuck in the 18th century, & always will be, while most of the world has >>>>>>>>>>> moved on to democracy. >>>>>>>>>>> >>>>>>>>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> Can Condorcet be weakened to comply with participation? >>>>>>>>>>>> Condorcet methods have plenty of advantages, but systems failing >>>>>>>>>>>> participation are vulnerable to court challenges or being struck down as >>>>>>>>>>>> unconstitutional, as seen in Germany. >>>>>>>>>>>> ---- >>>>>>>>>>>> Election-Methods mailing list - see https://electorama.com/em >>>>>>>>>>>> for list info >>>>>>>>>>>> >>>>>>>>>>>

My current line of thinking is that you could say a candidate needs a pairwise supermajority, rather than just a majority, for a defeat to count as a "real defeat" instead of a tie. Perhaps there's some way to choose this margin that guarantees no participation failures? On Fri, Mar 1, 2024 at 9:48 PM Closed Limelike Curves < closed.limelike.curves@gmail.com> wrote: > But Steve is right: For any one of us, the minuscule chance of a >> preference of ours being negatively responded-to doesn’t even come close to >> outweighing the strategy-freeness for which RP(wv) is being used. >> > Agree that if RP improves strategy-resistance in practice, a tiny risk of > participation failures is worth it. But courts might not agree. More > importantly, it means you can't challenge IRV in court on the basis that > participation/monotonicity failure violates a fundamental human right (if > your own proposed alternative also violates that right). > > That occurred to me too. Well I’d say that the important thing is that >> after the illegal Participation-failure result is discarded, then even if >> IA gives the same winner, this time it didn’t happen as a >> Participation-violation. >> > It's still a participation violation--the whole combined electoral system > violates participation, even if the specific steps don't. In the same way, > there's no individual step of IRV that violates participation (each round > is just a plurality vote). It's the process as a whole that does. > > On Fri, Mar 1, 2024 at 7:49 PM Michael Ossipoff <email9648742@gmail.com> > wrote: > >> Yes, just a matter of, for each voter, decrementing the population-total >> of every pairwise-preference s/he voted. …& applying RP(wv) to that >> modified population preference-totals set. But, other than looking at that >> voter’s ballot, no new votecounting is needed. >> >> The entire Participation-check only takes half as long as the original >> exhaustive pairwise-count used by Condorcet. >> >> >> >>> Couldn't this new procedure still violate participation? >>> >> >> Not if it’s Implicit-Approval (ranked = approved). >> >> >> What if adding ballots[i] with A>B would cause B>A, but B also happens >>> to win under implicit approval voting? >>> >> >> That occurred to me too. Well I’d say that the important thing is that >> after the illegal Participation-failure result is discarded, then even if >> IA gives the same winner, this time it didn’t happen as a >> Participation-violation. >> >> The discarding makes the election innocent. >> >> But Steve is right: For any one of us, the minuscule chance of a >> preference of ours being negatively responded-to doesn’t even come close to >> outweighing the strategy-freeness for which RP(wv) is being used. >> >>> >>> >>> On Thu, Feb 29, 2024 at 4:02 PM Michael Ossipoff <email9648742@gmail.com> >>> wrote: >>> >>>> Yes, I too feel that though Consistency-failure is an embarrassment, >>>> it’s Participation-failure—where a particular voter should have stayed >>>> home—that is the rights-violation. >>>> >>>> Yes, maybe there’s some big subset of the voters, say 37%, such that, >>>> if they’d stayed home the result of applying the method to the other 63% >>>> (which would then have been the actual election-result) would have been the >>>> same as the result of applying it to them separately…but, because they >>>> voted, a different result happened. >>>> >>>> That doesn’t sound as bad as Participation-failure. >>>> >>>> 1. That 37%’s hypothetical collective-choice by the method isn’t as >>>> definite & stark as a person’s expressed-preference. >>>> >>>> 2. A *different outcome* from the hypothetical result of applying the >>>> method to the 37% isn’t as concretely clearly wrong as outright >>>> negative-response to someone’s expressed preference. >>>> >>>> …& that’s a good thing, because checking for Consistency-failure is >>>> what DOES sound computationally infeasible due to the many ways of dividing >>>> a large electorate into 2 par. >>>> >>>> Checking for Participation-failure would just be a matter of, for each >>>> voter, doing the count without hir ballot & determining whether that >>>> changes the winner to someone s/he ranked above the actual winner. >>>> >>>> With 300,000,000 voters that isn’t infeasible with today’s computers is >>>> it? >>>> >>>> I should have asked: >>>> >>>> In Germany, is Consistency-failure unconstitutional? That might be a >>>> problem for Condorcet. If only Participation-failure is unconstitutional, >>>> then wouldn’t Kobe computationally-feasible to check for that? >>>> >>>> When a Participation-failure is found, then elect the winner by >>>> Implicit-Approval. >>>> >>>> In wv, not ranking candidates you don’t like is good defensive-strategy >>>> anyway. If it’s known that many people vote that way, wv’s already good >>>> burial-deterrence is further enhanced. >>>> >>>> >>>> >>>> On Thu, Feb 29, 2024 at 10:06 Closed Limelike Curves < >>>> closed.limelike.curves@gmail.com> wrote: >>>> >>>>> That seems to exclude participation failures except in the case >>>>> of near-ties; I think adding a batch of ballots, all of which rank A>B, >>>>> shouldn't cause B to defeat A. >>>>> >>>>> I don't think we need perfect consistency, just participation. >>>>> Consistency failures are paradoxical, but consistency is a very >>>>> strong criterion and isn't needed for the weaker case of participation >>>>> (which limits consistency to the ). It's also strong enough that it >>>>> could lock you into Kemeny-Young (the unique order-consistent Condorcet >>>>> method). >>>>> >>>>> Checking for participation naively definitely isn't feasible, so we'd >>>>> need a more elegant approach. >>>>> >>>>> Alternatively, we could try finding a Condorcet system that violates >>>>> participation "as little as possible," in the sense that any participation >>>>> failures are forced by Condorcet-compliance. A judge might be willing >>>>> to sign off on that, since it's a tradeoff between two similarly-important >>>>> values (equal protection and majority rule). >>>>> >>>>> On Wed, Feb 28, 2024 at 10:30 PM Michael Ossipoff < >>>>> email9648742@gmail.com> wrote: >>>>> >>>>>> Maybe it might be good enough to just require that there must not be >>>>>> a Participation-violation with respect to any one of the voters, had s/he >>>>>> voted last? >>>>>> >>>>>> On Wed, Feb 28, 2024 at 22:17 Michael Ossipoff < >>>>>> email9648742@gmail.com> wrote: >>>>>> >>>>>>> Well I don’t know if the Consistency-check would be >>>>>>> Computationally-feasible, because of course there are a lot of ways to >>>>>>> divide a large electorate into 2 parts. >>>>>>> >>>>>>> That might be one more good reason to use Approval instead, for >>>>>>> those single-winner elections. >>>>>>> >>>>>>> On Wed, Feb 28, 2024 at 22:07 Michael Ossipoff < >>>>>>> email9648742@gmail.com> wrote: >>>>>>> >>>>>>>> I call RP(wv) with that modification “Nonsense-Free RP(wv)”, & >>>>>>>> propose it for Germany’s single-winner elections, including the single >>>>>>>> member district elections in their Additional-Member proportional >>>>>>>> topping-up Parliamentary elections. >>>>>>>> >>>>>>>> On Wed, Feb 28, 2024 at 21:47 Michael Ossipoff < >>>>>>>> email9648742@gmail.com> wrote: >>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> On Wed, Feb 28, 2024 at 21:07 Closed Limelike Curves < >>>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> . Some alternative criterion that gets us "99% of the way to >>>>>>>>>>> Condorcet," so it behaves like Condorcet except in the rare cases where it >>>>>>>>>>> conflicts with participation (or maybe just mono-add-top/remove-bottom). >>>>>>>>>> >>>>>>>>>> >>>>>>>>> There might be better ways, but there’s always the lexicographical >>>>>>>>> way. The criterion could require that Participation (& other >>>>>>>>> non-opposite-response criteria) & Consistency be met. …& that the voted >>>>>>>>> CW, when there is one must be elected when that doesn’t conflict with the >>>>>>>>> above requirements. >>>>>>>>> >>>>>>>>> A complying method could just repeat that wording, along with a >>>>>>>>> specification about what to do if there’s no voted CW, & what to do if the >>>>>>>>> ballot-configuration is such that additional of a new ballot could violate >>>>>>>>> Participation, or if some division of the electorate into 2 parts could >>>>>>>>> show a Consistency violation. >>>>>>>>> >>>>>>>>> Maybe apply Implicit-Approval to the ballots then. (Ranked = >>>>>>>>> approved) >>>>>>>>> >>>>>>>>>> >>>>>>>>>> On Wed, Feb 28, 2024 at 8:57 PM Closed Limelike Curves < >>>>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> It’s surprising that participation-violation is unconstitutional >>>>>>>>>>>> in Germany, because, here, even Hare’s greater nonmonotonicity is okay. >>>>>>>>>>>> >>>>>>>>>>> I'm actually not sure it is--the Supreme Court has never ruled >>>>>>>>>>> on , and courts also haven't ruled on the constitutionality of non-monotone >>>>>>>>>>> voting rules. STV has been upheld as constitutional in the past, but the >>>>>>>>>>> challenges were never brought over monotonicity failures. It's entirely >>>>>>>>>>> possible a new challenge could overturn it; there's a strong argument that >>>>>>>>>>> monotonicity failures violate due process and the equal protection clause. >>>>>>>>>>> >>>>>>>>>>> The ideal case to bring to the Supreme Court would have been for >>>>>>>>>>> Begich's campaign to sue after the 2022 Alaska election. A moderate >>>>>>>>>>> Republican plaintiff is appealing to the mostly-Republican Supreme >>>>>>>>>>> Court, without being too controversial. Being the Condorcet winner makes >>>>>>>>>>> his case look even stronger. >>>>>>>>>>> >>>>>>>>>>> On the other hand, if someone says the word "monotonicity" in >>>>>>>>>>> front of a judge, their eyes will glaze over and they'll immediately stop >>>>>>>>>>> caring about all this weird, complicated nerd math. The way to explain >>>>>>>>>>> participation failures is to run a ton of ads explaining to Alaska >>>>>>>>>>> Republicans that Begich lost because *he got* *too many votes. * >>>>>>>>>>> >>>>>>>>>>> One suggestion: why not rename monotonicity to "helpfulness?" >>>>>>>>>>> (Voting should help your candidate, not hurt them). We can call >>>>>>>>>>> monotonicity failures "spitefulness" (because the system is going out of >>>>>>>>>>> its way to do the opposite of what you ask it to). >>>>>>>>>>> >>>>>>>>>>> On Wed, Feb 28, 2024 at 11:32 AM Michael Ossipoff < >>>>>>>>>>> email9648742@gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> It’s surprising that participation-violation is >>>>>>>>>>>> unconstitutional in Germany, because, here, even Hare’s greater >>>>>>>>>>>> nonmonotonicity is okay. >>>>>>>>>>>> >>>>>>>>>>>> It’s disingenuous to say that Hare is nonmonotonic & Condorcet >>>>>>>>>>>> isn’t. Nonmonotonicity is just defined to give Condorcet, with it’s >>>>>>>>>>>> participation-failure, a pass. >>>>>>>>>>>> >>>>>>>>>>>> I’ve heard that Participation & the Condorcet Criterion are >>>>>>>>>>>> mutually incompatible. I feel that participation-failure is an acceptable >>>>>>>>>>>> price for the Condorcet Criterion. Always electing the voted CW brings >>>>>>>>>>>> strategy improvement, & the unpredictable & rare participation-failure is >>>>>>>>>>>> probably irrelevant to strategy. >>>>>>>>>>>> >>>>>>>>>>>> But that incompatibility, along with the ones Arrow >>>>>>>>>>>> pointed-out, shows that single-winner elections aren’t perfect. …making a >>>>>>>>>>>> good argument for PR…*monotonic* PR, which excludes STV & Largest-Remainder. >>>>>>>>>>>> >>>>>>>>>>>> Maybe, as a PR country (like 2/3 of the world’s countries), >>>>>>>>>>>> Germany feels no need to compromise participation. >>>>>>>>>>>> >>>>>>>>>>>> We’re told that list-PR “hasn’t been tried”. No, just in 2/3 of >>>>>>>>>>>> the world’s countries for about a century. >>>>>>>>>>>> >>>>>>>>>>>> But, with that counterfactual “hasn’t been tried” excuse, we’re >>>>>>>>>>>> stuck in the 18th century, & always will be, while most of the world has >>>>>>>>>>>> moved on to democracy. >>>>>>>>>>>> >>>>>>>>>>>> On Wed, Feb 28, 2024 at 10:36 Closed Limelike Curves < >>>>>>>>>>>> closed.limelike.curves@gmail.com> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> Can Condorcet be weakened to comply with participation? >>>>>>>>>>>>> Condorcet methods have plenty of advantages, but systems failing >>>>>>>>>>>>> participation are vulnerable to court challenges or being struck down as >>>>>>>>>>>>> unconstitutional, as seen in Germany. >>>>>>>>>>>>> ---- >>>>>>>>>>>>> Election-Methods mailing list - see https://electorama.com/em >>>>>>>>>>>>> for list info >>>>>>>>>>>>> >>>>>>>>>>>>