Hi Jameson, It's always good to see people thinking on these problems and trying to come up with solutions. > MAS is good at dealing with a vote-splitting situation ("chicken dilemma"... I've not heard of the Chicken Dilemma before and found a definition at http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion. Now I'm more confused because in my opinion, candidate B should win the election described. It is looking to me like the Chicken Dilemma is just a test to see if a voting system is susceptible to bullet voting. In that case, every system except plurality fails this criteria. Am I missing something? On Mon, Oct 10, 2016 at 10:24 PM, <election-methods-owner@lists.electorama.com> wrote: > Only subscribers are allowed to post to this mailing list. Please > visit the following location for information on subscribing: > http://www.electorama.com/em > > > > ---------- Forwarded message ---------- > From: Brian Kelly <bkelly1984@gmail.com> > To: The Center for Election Science <electionscience@googlegroups.com> > Cc: election-methods@lists.electorama.com > Date: Mon, 10 Oct 2016 21:24:05 -0700 (PDT) > Subject: Re: MAS defined. > Hi Jameson, > > It's always good to see people thinking on these problems and trying to come up with solutions. > >> MAS is good at dealing with a vote-splitting situation ("chicken dilemma"... > > I've not heard of the Chicken Dilemma before and found a definition at http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion. Now I'm more confused because in my opinion, candidate B should win the election described. > > It is looking to me like the Chicken Dilemma is just a test to see if a voting system is susceptible to bullet voting. In that case, every system except plurality fails this criteria. > > Am I missing something? > > > > On Thursday, October 6, 2016 at 12:41:41 PM UTC-6, Jameson Quinn wrote: >> >> I've been working on a simple three-slot system as a next step after approval. This has gone through various iterations and names: U/P, MUMA, NUMA. The latest, and I hope final, version is MAS, Majority Acceptable Score. Here's an explanation, intended for those without a voting theory background. The basic system is described in 3 sentences in the first paragraph; the second paragraph describes the default rule, which is worthwhile but not absolutely essential to the system; and the next two paragraphs give some scenarios. >> >> For each candidate, you may upvote, “midvote”, or downvote. Candidates with a majority of downvotes are eliminated, unless that eliminates everyone. The remaining candidates get 2 points for every upvote and 1 for every midvote. Most points wins. >> >> When people leave a candidate blank, that could mean one of two things: “never heard of this person”, which should count as a downvote for safety; or “no strong feelings”, which should count as a midvote (because if the voter really disliked the candidate they would have downvoted). To distinguish these possibilities, see if the candidate’s score from non-blank votes averages at least half a point per voter; for instance, this would be true if they were upvoted by 25%, or explicitly midvoted by 50%. If the score is this good, that candidate is reasonably well-known and well-liked, so blanks count as midvotes; if it isn’t, that candidate is relatively unknown, so blanks count as downvotes. >> >> MAS is good at dealing with a vote-splitting situation ("chicken dilemma", so called because in many voting systems it can work like a game of chicken between the two majority subfactions). Say that one "side" of voters have 55%, but there are two candidates on that side splitting the vote and only one on the other side. In this case, assuming voters on either side downvote the candidates on the other side, the 45% candidate will be eliminated by downvotes, and whichever subfaction of the majority has more supporters will win. >> >> MAS also deals well with a "center squeeze" scenario, in which a centrist candidate faces off against candidates on either side. Assuming all three are equally qualified and likeable, the centrist will probably be able to beat either side in a one-on-one race (because leftist voters will prefer Center over Right, and vice versa); but it is quite possible that there will be more partisans on either side than in the center. In this case, the centrist should not be punished simply for being more "crowded" ideologically; their ability to dominate one-on-one means they should win. But many voting systems, such as IRV, can eliminate the centrist prematurely, giving results like the tragic outcome in Egypt 2012. Meanwhile, other systems, such as Condorcet, can enable tricky strategies by one side to possibly win. In MAS, as long as the center candidate was preferred by a respectable number of voters (say, 20% or more), "midvotes" from voters in either wing would probably be enough to let the centrist win; and either defensive "midvoting" from the weaker wing or defensive "downvoting" by the centrists would probably be enough to stop a takeover by the stronger wing. > >

I reread the Chicken Dilemma Criterion article in the spirit of "of course B should win". To me the weak point in the article seemed to be the sentence "The B voters refuse to vote A over anyone". The description did not clearly express the underlying assumption that A and B candidates and voters actually are very close to each others (similar minded). A voters sincerely like B much more than C, and B voters sincerely like A much more than C. A and B voters together have majority over the C voters, and therefore one of them ("the AB team") should win. Because A is more popular than B, A should win. But B voters are strategical and therefore "refuse" to vote sincerely, and decide not to rank A above C. In a good election method this strategy should preferably not work. There is a risk that both A and B voters "refuse" to support B and A respectively (not rank them second as they should), and as a result their worst alternative (C) could win. Did this explanation make the philosophy of the "chicken style" criteria clearer? B should not win since if B would win by using this strategy, that could encourage also A supporters to do the same, and the whole election could become a mess where the winner would be quite random (depending on how many voters of each group voted strategically). Note that the number of A and B voters could be about the same, and A and B voters would not know which group would benefit of applying the "refusal" strategy. Juho > On 11 Oct 2016, at 09:00, Brian Kelly <bkelly1984@gmail.com> wrote: > > Hi Jameson, > > It's always good to see people thinking on these problems and trying > to come up with solutions. > >> MAS is good at dealing with a vote-splitting situation ("chicken dilemma"... > > I've not heard of the Chicken Dilemma before and found a definition at > http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion. Now I'm > more confused because in my opinion, candidate B should win the > election described. > > It is looking to me like the Chicken Dilemma is just a test to see if > a voting system is susceptible to bullet voting. In that case, every > system except plurality fails this criteria. > > Am I missing something? > > On Mon, Oct 10, 2016 at 10:24 PM, > <election-methods-owner@lists.electorama.com> wrote: >> Only subscribers are allowed to post to this mailing list. Please >> visit the following location for information on subscribing: >> http://www.electorama.com/em >> >> >> >> ---------- Forwarded message ---------- >> From: Brian Kelly <bkelly1984@gmail.com> >> To: The Center for Election Science <electionscience@googlegroups.com> >> Cc: election-methods@lists.electorama.com >> Date: Mon, 10 Oct 2016 21:24:05 -0700 (PDT) >> Subject: Re: MAS defined. >> Hi Jameson, >> >> It's always good to see people thinking on these problems and trying to come up with solutions. >> >>> MAS is good at dealing with a vote-splitting situation ("chicken dilemma"... >> >> I've not heard of the Chicken Dilemma before and found a definition at http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion. Now I'm more confused because in my opinion, candidate B should win the election described. >> >> It is looking to me like the Chicken Dilemma is just a test to see if a voting system is susceptible to bullet voting. In that case, every system except plurality fails this criteria. >> >> Am I missing something? >> >> >> >> On Thursday, October 6, 2016 at 12:41:41 PM UTC-6, Jameson Quinn wrote: >>> >>> I've been working on a simple three-slot system as a next step after approval. This has gone through various iterations and names: U/P, MUMA, NUMA. The latest, and I hope final, version is MAS, Majority Acceptable Score. Here's an explanation, intended for those without a voting theory background. The basic system is described in 3 sentences in the first paragraph; the second paragraph describes the default rule, which is worthwhile but not absolutely essential to the system; and the next two paragraphs give some scenarios. >>> >>> For each candidate, you may upvote, “midvote”, or downvote. Candidates with a majority of downvotes are eliminated, unless that eliminates everyone. The remaining candidates get 2 points for every upvote and 1 for every midvote. Most points wins. >>> >>> When people leave a candidate blank, that could mean one of two things: “never heard of this person”, which should count as a downvote for safety; or “no strong feelings”, which should count as a midvote (because if the voter really disliked the candidate they would have downvoted). To distinguish these possibilities, see if the candidate’s score from non-blank votes averages at least half a point per voter; for instance, this would be true if they were upvoted by 25%, or explicitly midvoted by 50%. If the score is this good, that candidate is reasonably well-known and well-liked, so blanks count as midvotes; if it isn’t, that candidate is relatively unknown, so blanks count as downvotes. >>> >>> MAS is good at dealing with a vote-splitting situation ("chicken dilemma", so called because in many voting systems it can work like a game of chicken between the two majority subfactions). Say that one "side" of voters have 55%, but there are two candidates on that side splitting the vote and only one on the other side. In this case, assuming voters on either side downvote the candidates on the other side, the 45% candidate will be eliminated by downvotes, and whichever subfaction of the majority has more supporters will win. >>> >>> MAS also deals well with a "center squeeze" scenario, in which a centrist candidate faces off against candidates on either side. Assuming all three are equally qualified and likeable, the centrist will probably be able to beat either side in a one-on-one race (because leftist voters will prefer Center over Right, and vice versa); but it is quite possible that there will be more partisans on either side than in the center. In this case, the centrist should not be punished simply for being more "crowded" ideologically; their ability to dominate one-on-one means they should win. But many voting systems, such as IRV, can eliminate the centrist prematurely, giving results like the tragic outcome in Egypt 2012. Meanwhile, other systems, such as Condorcet, can enable tricky strategies by one side to possibly win. In MAS, as long as the center candidate was preferred by a respectable number of voters (say, 20% or more), "midvotes" from voters in either wing would probably be enough to let the centrist win; and either defensive "midvoting" from the weaker wing or defensive "downvoting" by the centrists would probably be enough to stop a takeover by the stronger wing. >> >> > ---- > Election-Methods mailing list - see http://electorama.com/em for list info

1. Some voting systems, such as approval voting, ignore the problem.
Perhaps the assumption here is that it will be impossible to organize a
defection without prompting a retaliation, and thus that both sides will
prefer to cooperate. ("Mutual assured destruction"?)


1. Some voting systems, such as Majority Choice Approval
<http://wiki.electorama.com/wiki/Majority_Choice_Approval>, try
exploit the fact that each faction is not a single coordinated entity, but
a group of individual voters. The idea is that if a small number of voters
defect, they should be ignored; hopefully, in that situation, majority
cooperation will be a stable strategy.


1. Other voting systems, such as ICT
<http://wiki.electorama.com/w/index.php?title=ICT&action=edit&redlink=1>,
try to exploit the fact that in a real-world election, A and B are never
perfectly balanced; one subfaction is always larger. In this case, a voting
system can encourage the smaller group to cooperate by threatening to elect
C (punishing both groups) if the smaller group defects. The criterion below
is passed only by this kind of voting system.

I've edited the Chicken Dilemma Criterion article to include the following introductory text: > One type of election scenario which is particularly fraught is when there > is a majority split into two subfactions (below called A and B), competing > against a united minority (below called C) that is bigger than either of > the subfactions. This scenario has been called the "chicken dilemma" > because in many election systems, the two majority subfactions are in a > situation that resembles the classic "chicken" or "snowdrift game > (especially if voters are not sure which of the two subfactions is larger). > That is, if we assume each faction has a single, coordinated strategy > defined as "cooperate" (vote both candidates A and B above bottom) or > "defect" (bullet vote, with only the favorite above bottom); and that each > faction values its preferred choice at 10, its less-preferred choice at 8, > and candidate C at 0, many voting systems lead to the following payoff > matrix: > cooperate defect > cooperate 9, 9 8, 10 > defect 10, 9 0, 0 > *Fig. 2: Chicken with numericalpayoffs > <http://wiki.electorama.com/w/index.php?title=Risk_dominance&action=edit&redlink=1>*There > are various ways to deal with this situation. For instance: > > 1. Some voting systems, such as approval voting, ignore the problem. > Perhaps the assumption here is that it will be impossible to organize a > defection without prompting a retaliation, and thus that both sides will > prefer to cooperate. ("Mutual assured destruction"?) > > > 1. Some voting systems, such as Majority Choice Approval > <http://wiki.electorama.com/wiki/Majority_Choice_Approval>, try > exploit the fact that each faction is not a single coordinated entity, but > a group of individual voters. The idea is that if a small number of voters > defect, they should be ignored; hopefully, in that situation, majority > cooperation will be a stable strategy. > > > 1. Other voting systems, such as ICT > <http://wiki.electorama.com/w/index.php?title=ICT&action=edit&redlink=1>, > try to exploit the fact that in a real-world election, A and B are never > perfectly balanced; one subfaction is always larger. In this case, a voting > system can encourage the smaller group to cooperate by threatening to elect > C (punishing both groups) if the smaller group defects. The criterion below > is passed only by this kind of voting system. > > MAS of course would be in group 2. Personally, I prefer group 2 to group 3, because group 3 can misread a center squeeze scenario as a failed chicken dilemma, and decide to "punish" the "betrayers" by electing the true Condorcet loser. 2016-10-11 6:22 GMT-04:00 Juho Laatu <juho.laatu@gmail.com>: > I reread the Chicken Dilemma Criterion article in the spirit of "of course > B should win". To me the weak point in the article seemed to be the > sentence "The B voters refuse to vote A over anyone". The description did > not clearly express the underlying assumption that A and B candidates and > voters actually are very close to each others (similar minded). A voters > sincerely like B much more than C, and B voters sincerely like A much more > than C. A and B voters together have majority over the C voters, and > therefore one of them ("the AB team") should win. Because A is more popular > than B, A should win. But B voters are strategical and therefore "refuse" > to vote sincerely, and decide not to rank A above C. In a good election > method this strategy should preferably not work. There is a risk that both > A and B voters "refuse" to support B and A respectively (not rank them > second as they should), and as a result their worst alternative (C) could > win. > > Did this explanation make the philosophy of the "chicken style" criteria > clearer? > > B should not win since if B would win by using this strategy, that could > encourage also A supporters to do the same, and the whole election could > become a mess where the winner would be quite random (depending on how many > voters of each group voted strategically). Note that the number of A and B > voters could be about the same, and A and B voters would not know which > group would benefit of applying the "refusal" strategy. > > Juho > > > > > On 11 Oct 2016, at 09:00, Brian Kelly <bkelly1984@gmail.com> wrote: > > > > Hi Jameson, > > > > It's always good to see people thinking on these problems and trying > > to come up with solutions. > > > >> MAS is good at dealing with a vote-splitting situation ("chicken > dilemma"... > > > > I've not heard of the Chicken Dilemma before and found a definition at > > http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion. Now I'm > > more confused because in my opinion, candidate B should win the > > election described. > > > > It is looking to me like the Chicken Dilemma is just a test to see if > > a voting system is susceptible to bullet voting. In that case, every > > system except plurality fails this criteria. > > > > Am I missing something? > > > > On Mon, Oct 10, 2016 at 10:24 PM, > > <election-methods-owner@lists.electorama.com> wrote: > >> Only subscribers are allowed to post to this mailing list. Please > >> visit the following location for information on subscribing: > >> http://www.electorama.com/em > >> > >> > >> > >> ---------- Forwarded message ---------- > >> From: Brian Kelly <bkelly1984@gmail.com> > >> To: The Center for Election Science <electionscience@googlegroups.com> > >> Cc: election-methods@lists.electorama.com > >> Date: Mon, 10 Oct 2016 21:24:05 -0700 (PDT) > >> Subject: Re: MAS defined. > >> Hi Jameson, > >> > >> It's always good to see people thinking on these problems and trying to > come up with solutions. > >> > >>> MAS is good at dealing with a vote-splitting situation ("chicken > dilemma"... > >> > >> I've not heard of the Chicken Dilemma before and found a definition at > http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion. Now I'm more > confused because in my opinion, candidate B should win the election > described. > >> > >> It is looking to me like the Chicken Dilemma is just a test to see if a > voting system is susceptible to bullet voting. In that case, every system > except plurality fails this criteria. > >> > >> Am I missing something? > >> > >> > >> > >> On Thursday, October 6, 2016 at 12:41:41 PM UTC-6, Jameson Quinn wrote: > >>> > >>> I've been working on a simple three-slot system as a next step after > approval. This has gone through various iterations and names: U/P, MUMA, > NUMA. The latest, and I hope final, version is MAS, Majority Acceptable > Score. Here's an explanation, intended for those without a voting theory > background. The basic system is described in 3 sentences in the first > paragraph; the second paragraph describes the default rule, which is > worthwhile but not absolutely essential to the system; and the next two > paragraphs give some scenarios. > >>> > >>> For each candidate, you may upvote, “midvote”, or downvote. Candidates > with a majority of downvotes are eliminated, unless that eliminates > everyone. The remaining candidates get 2 points for every upvote and 1 for > every midvote. Most points wins. > >>> > >>> When people leave a candidate blank, that could mean one of two > things: “never heard of this person”, which should count as a downvote for > safety; or “no strong feelings”, which should count as a midvote (because > if the voter really disliked the candidate they would have downvoted). To > distinguish these possibilities, see if the candidate’s score from > non-blank votes averages at least half a point per voter; for instance, > this would be true if they were upvoted by 25%, or explicitly midvoted by > 50%. If the score is this good, that candidate is reasonably well-known and > well-liked, so blanks count as midvotes; if it isn’t, that candidate is > relatively unknown, so blanks count as downvotes. > >>> > >>> MAS is good at dealing with a vote-splitting situation ("chicken > dilemma", so called because in many voting systems it can work like a game > of chicken between the two majority subfactions). Say that one "side" of > voters have 55%, but there are two candidates on that side splitting the > vote and only one on the other side. In this case, assuming voters on > either side downvote the candidates on the other side, the 45% candidate > will be eliminated by downvotes, and whichever subfaction of the majority > has more supporters will win. > >>> > >>> MAS also deals well with a "center squeeze" scenario, in which a > centrist candidate faces off against candidates on either side. Assuming > all three are equally qualified and likeable, the centrist will probably be > able to beat either side in a one-on-one race (because leftist voters will > prefer Center over Right, and vice versa); but it is quite possible that > there will be more partisans on either side than in the center. In this > case, the centrist should not be punished simply for being more "crowded" > ideologically; their ability to dominate one-on-one means they should win. > But many voting systems, such as IRV, can eliminate the centrist > prematurely, giving results like the tragic outcome in Egypt 2012. > Meanwhile, other systems, such as Condorcet, can enable tricky strategies > by one side to possibly win. In MAS, as long as the center candidate was > preferred by a respectable number of voters (say, 20% or more), "midvotes" > from voters in either wing would probably be enough to let the centrist > win; and either defensive "midvoting" from the weaker wing or defensive > "downvoting" by the centrists would probably be enough to stop a takeover > by the stronger wing. > >> > >> > > ---- > > Election-Methods mailing list - see http://electorama.com/em for list > info > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >

I've been thinking about default rules for MAS. Some desirable characteristics for a default rule are: -Should ensure that weak candidates don't win simply because all the stronger candidates were eliminated. -Should default to cooperation in a chicken dilemma with lazy voters. -Should be summable. -Should be easy to describe. -Should make intuitive sense when described. Here's the best I can do in terms of those criteria: Each candidate's "expected downvotes" will be the number of upvotes for candidates with a higher explicit score, minus half their explicit midvotes. (This "half" could be any number between 0 and 1, under the theory that some, but not all, of their explicit midvotes will come from voters who upvoted candidates with a higher explicit score.) Their blank votes will be counted as implicit downvotes until their total downvotes reaches their expected downvotes; after that, blank votes will be counted as implicit midvotes. Almost-pathological scenario pair: S1: 25: A(>B) 25: B(>A) 4: B>A 46: C(>>A,B) vs.: 25: A(>B) 29: B(>A) 10: C>A 36: C(>>A,B) In scenario 1, A gets 44 implicit downvotes, thus 27 implicit midvotes. Score is thus 2*25+4+27=81. B gets 46 implicit downvotes, thus 25 implicit midvotes. Score is thus 30*2+25 = 85. B wins; correctly, I'd argue (B is CW). In scenario 2, A gets 41 implicit downvotes, thus 24 implicit midvotes. Score is 2*25+24+10 = 84. B gets 46 implicit downvotes, thus 25 implicit midvotes. Score is 2*29+25=83. A wins; again, this correctly found the CW. Now, obviously, because this is working summably, there's no way for the method to actually know whether the midvotes for A come from B voters (in which case they don't change the CW from B) or from C voters (in which case, they do). But I think that these scenarios are realistic in one sense: if the C voters really do tend to prefer A over B, that will lead to more explicit A midvotes than any realistic differential midvoting from the A and B groups. Thus, while you could easily adjust either the above scenarios to give the non-CW, I think that kind of result would be relatively implausible.