To EM: Please check the following [clarifications or corrections written within the square brackets]. Currently I see these suggestions as more clearly expressing B&L’s own intentions in the following two extracts from M. Balinski and R. Laraki (2011) Majority Judgment, MIT. Please explain if you think I have misunderstood these paragraphs: p.14: Similar reasoning shows that the majority-grade mechanism is group strategy-proof-in-grading. A group of voters who share the same beliefs (e.g. they belong to the same political party) has the same optimal strategy, namely, to give to the candidates the grades it believes they merit. For if the group believed that Royal merited better than Good, and all raised the grade they gave her, her majority-gauge would remain the same (p does not change) [her majority-gauge would probably only be changed insignificantly when thousands are voting (p would probably only be changed insignificantly)]. If all lowered the grade they gave her, her majority-gauge would decrease (q increases), and perhaps her majority-grade would be lowered (not their intent). If [instead] the group believed that Royal merited worse than Good, and all lowered the grade they gave her, her majority-gauge would remain the same (q does not change) [her majority-gauge would probably only be changed insignificantly when thousands are voting (q would probably only be increased insignificantly)]. If [instead] all raised the grade they gave her, her majority-gauge would increase (p increases),and perhaps her majority-grade would be raised (not their intent). p.15: One means by which it [MJ] resists [manipulation] is easy to explain. Take the example of Bayrou with a Good+ and Royal with a Good− (see table 1.4); their respective majority-gauges are Bayrou: (44.3%, Good, 30.6%) Royal: (39.4%, Good, 41.5%). [Given these two majority-guages] How could a voter who graded Royal higher than Bayrou manipulate? By changing the grades assigned to try to lower Bayrou’s majority-gauge and to raise Royal’s majority-gauge. But the majority judgment is partially strategy-proof-in- ranking: those voters who can [might marginally be able to] lower Bayrou’s majority-gauge cannot [significantly] raise Royal’s, and those who can [might marginally be able to] raise Royal’s majority-gauge cannot [significantly] lower Bayrou’s. For suppose a voter can lower Bayrou’s. Then she must have given Bayrou a Good or better; but having preferred Royal to Bayrou, the voter [she probably] gave a grade of better than Good to Royal, so she cannot raise Royal’s majority-gauge [significantly] (cannot [significantly] raise her p). Symmetrically, a [different] voter who can raise [no, lower] Royal’s majority-gauge must have given her a Good or worse and thus to Bayrou a worse [no, a better] than Good; so the voter cannot lower [no, raise] Bayrou’s majority-gauge [significantly] (cannot [significantly]increase his q [p]). Compared with other mechanisms, the majority judgment cuts in half the possibility of manipulation, however bizarre a voter’s motivations or whatever her utility function. The majority judgment resists manipulation in still other ways that other methods do not, but to see how requires information found in voters’ individual ballots that is not shown in the elections results of table 1.4. For example, significant numbers of voters cannot contribute at all either to raising Royal’s majority-gauge or to lowering Bayrou’s (28% of those who graded Royal above Bayrou). Moreover, those who can manipulate have no incentive to exaggerate very much in any case, for it does not pay to do so (a more detailed analysis is given in chapter 19). ++++++++++++++++ Note: If you wish to receive a copy of the whole chapter as an attachment, just ask (stevebosworth@hotmail.com). I look forward to your comments. Steve

On 01/03/2017 08:44 PM, steve bosworth wrote: > To EM: > > Please check the following [clarifications or corrections written within > the square brackets]. Currently I see these suggestions as more clearly > expressing B&L’s own intentions in the following two extracts from M. > Balinski and R. Laraki (2011) /Majority Judgment/, MIT. Please explain > if you think I have misunderstood these paragraphs: > > p.14: > > Similar reasoning shows that the majority-grade mechanism is /group/ > > /strategy-proof-in-grading/. A group of voters who share the same > beliefs (e.g. > > they belong to the same political party) has the same optimal strategy, > namely, to > > give to the candidates the grades it believes they merit. For if the > group believed > > that Royal merited better than /Good/, and all raised the grade they > gave her, > > her majority-gauge would remain the same (/p /does not change) [her > majority-gauge would probably only be changed insignificantly when > thousands are voting (/p would/ probably only be changed > insignificantly)]. If all lowered > > the grade they gave her, her majority-gauge would decrease (/q > /increases), and > > perhaps her majority-grade would be lowered (not their intent). If > [instead] the group > > believed that Royal merited worse than /Good/, and all lowered the grade > they > > gave her, her majority-gauge would remain the same (/q /does not change) > [her majority-gauge would probably only be changed insignificantly when > thousands are voting (q/would/ probably only be increased > insignificantly)]. If [instead] all > > raised the grade they gave her, her majority-gauge would increase (/p > /increases),and perhaps her majority-grade would be raised (not their > intent). Basically, you're right. Suppose that a group thinks Royal merits a Good. What B&L says is: - We want to show that the optimal strategy for this group is to give Royal a Good grade. - Suppose for contradiction they give Royal another grade, and compare this to what would happen if they gave Royal a Good. - If the other grade they gave is better than Good, either nothing changes (most likely when thousands are voting), or Royal gets a better majority grade than Good (which is not what the group wants). - If the other grade they gave is worse than Good, either nothing changes (ditto), or Royal gets a worse majority grade than Good (which is not what the group wants). - So if the group wants Royal's grade to be Good, giving Royal any other grade but Good only risks results the group doesn't want. - Thus, grading honestly is optimal. The point isn't that the voters are very unlikely to change the outcome, but rather that even when they change the outcome by voting dishonestly, they change it in a way that they don't benefit from. > p.15: > > One means by which it [MJ] resists [manipulation] is easy to explain. > Take the example of Bayrou with a /Good/+ and Royal with a /Good/− (see > table 1.4); their respective > > majority-gauges are > > > > Bayrou: (44.3%, /Good/, 30.6%) Royal: (39.4%, /Good/, 41.5%). > > > > [Given these two majority-guages] How could a voter who graded Royal > higher than Bayrou manipulate? By changing > > the grades assigned to try to lower Bayrou’s majority-gauge and to raise > > Royal’s majority-gauge. But the majority judgment is /partially > strategy-proof-in-/ > > /ranking/: those voters who can [might marginally be able to] lower > Bayrou’s majority-gauge cannot [significantly] raise > > Royal’s, and those who can [might marginally be able to] raise Royal’s > majority-gauge cannot [significantly] lower Bayrou’s. Again, the point here isn't directly that the outcome doesn't often change. (That the outcome doesn't often change is beneficial for other reasons, some of which are related to strategy.) The main point is instead: Suppose some voter ranks Royal above Bayrou, like this: Excellent | Good | Fair | Poor | Reject ..........|.Royal|.Bayrou.|......|....... Then if the voter wants to make Royal rather than Bayrou win, she can push Royal up or Bayrou down. But she can only push Bayrou down from where Bayrou is ranked on her honest ballot, and can only push Royal up from where Royal is ranked on her honest ballot. And in effect, this makes only half the ballot available to do either. If the voter has ranked Royal highly, she can push Bayrou down but can't move Royal even higher. On the other hand, if the voter has ranked Royal closer to the Reject end, she can push Royal higher (up to Excellent), but can't push Bayrou very far down. So a voter can only either exaggerate Royal (if she graded Royal low on the original ballot) or exaggerate Bayrou (if she graded Bayrou high), but not both at the same time. The example voter above has graded Royal pretty high and so can only exaggerate by one step - by moving Royal from Good to Excellent. On the other hand, she can move Bayrou all the way from Fair to Reject. > 1.4. For example, significant numbers of voters cannot contribute at all > either > > to raising Royal’s majority-gauge or to lowering Bayrou’s (28% of those who > > graded Royal above Bayrou). Moreover, those who can manipulate have no > > incentive to exaggerate very much in any case, for it does not pay to do > so (a > > more detailed analysis is given in chapter 19). Here you have something that's more related to the fact that MJ is robust. A large number of voters simply *can't* change Royal or Bayrou's majority gauge. This further helps with the strategy resistance beyond what they mentioned above.

On 01/04/2017 01:45 PM, Kristofer Munsterhjelm wrote: > On 01/03/2017 08:44 PM, steve bosworth wrote: >> To EM: >> >> Please check the following [clarifications or corrections written within >> the square brackets]. Currently I see these suggestions as more clearly >> expressing B&L’s own intentions in the following two extracts from M. >> Balinski and R. Laraki (2011) /Majority Judgment/, MIT. Please explain >> if you think I have misunderstood these paragraphs: >> >> p.14: >> >> Similar reasoning shows that the majority-grade mechanism is /group/ >> >> /strategy-proof-in-grading/. A group of voters who share the same >> beliefs (e.g. >> >> they belong to the same political party) has the same optimal strategy, >> namely, to >> >> give to the candidates the grades it believes they merit. For if the >> group believed >> >> that Royal merited better than /Good/, and all raised the grade they >> gave her, >> >> her majority-gauge would remain the same (/p /does not change) [her >> majority-gauge would probably only be changed insignificantly when >> thousands are voting (/p would/ probably only be changed >> insignificantly)]. If all lowered >> >> the grade they gave her, her majority-gauge would decrease (/q >> /increases), and >> >> perhaps her majority-grade would be lowered (not their intent). If >> [instead] the group >> >> believed that Royal merited worse than /Good/, and all lowered the grade >> they >> >> gave her, her majority-gauge would remain the same (/q /does not change) >> [her majority-gauge would probably only be changed insignificantly when >> thousands are voting (q/would/ probably only be increased >> insignificantly)]. If [instead] all >> >> raised the grade they gave her, her majority-gauge would increase (/p >> /increases),and perhaps her majority-grade would be raised (not their >> intent). > > Basically, you're right. I should clarify what I meant by that. You're right that the voters can only very rarely change the outcome. But the point beyond this observation is, as I said, that even when they can, it's detrimental for them to do so. That is assuming they're strategizing in grades, i.e. want Royal to get a Good rather than Royal to win.

  De : Kristofer Munsterhjelm <km_elmet@t-online.de>

Hi Kristofer, I realize you are only interpreting B&L, so I don't mean to shoot the messenger. De : Kristofer Munsterhjelm <km_elmet@t-online.de> À : steve bosworth <stevebosworth@hotmail.com>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> Envoyé le : Mercredi 4 janvier 2017 6h45 Objet : Re: [EM] Interpreting Balinski's MJ words >> /strategy-proof-in-grading/.  A group of voters who share the same >> beliefs (e.g. >> they belong to the same political party) has the same optimal strategy, >> namely, to >> give to the candidates the grades it believes they merit.  You clarified your original response to this in saying: >You're right that the voters can only very rarely change the outcome. >But the point beyond this observation is, as I said, that even when they >can, it's detrimental for them to do so. > >That is assuming they're strategizing in grades, i.e. want Royal to get >a Good rather than Royal to win. Do you find it easy to imagine a scenario where a group of like-minded voters has this as a strategic goal? At the very least, this description of the goal would be quite abbreviated from what the actual thought must be.There's no benefit in trying to give Royal a "Good" median rating if no scenario is envisioned where Royal could win with this rating.  >> One means by which it [MJ] resists [manipulation] is easy to explain. >> Take the example of Bayrou with a /Good/+ and Royal with a /Good/− (see >> table 1.4); their respective >> majority-gauges are >>   ... >> But the majority judgment is /partially >> strategy-proof-in-/ >> /ranking/: those voters who can [might marginally be able to] lower >> Bayrou’s majority-gauge cannot [significantly] raise >> Royal’s, and those who can [might marginally be able to] raise Royal’s >> majority-gauge cannot [significantly] lower Bayrou’s. >Again, the point here isn't directly that the outcome doesn't often >change. (That the outcome doesn't often change is beneficial for other >reasons, some of which are related to strategy.) > >The main point is instead: > >Suppose some voter ranks Royal above Bayrou, like this: > >Excellent | Good | Fair  | Poor | Reject >..........|.Royal|.Bayrou.|......|....... > >Then if the voter wants to make Royal rather than Bayrou win, she can >push Royal up or Bayrou down. > >But she can only push Bayrou down from where Bayrou is ranked on her >honest ballot, and can only push Royal up from where Royal is ranked on >her honest ballot. > >And in effect, this makes only half the ballot available to do either. >If the voter has ranked Royal highly, she can push Bayrou down but can't >move Royal even higher. On the other hand, if the voter has ranked Royal >closer to the Reject end, she can push Royal higher (up to Excellent), >but can't push Bayrou very far down. > >So a voter can only either exaggerate Royal (if she graded Royal low on >the original ballot) or exaggerate Bayrou (if she graded Bayrou high), >but not both at the same time. > >The example voter above has graded Royal pretty high and so can only >exaggerate by one step - by moving Royal from Good to Excellent. On the >other hand, she can move Bayrou all the way from Fair to Reject. This sounds like they are saying that it's a noteworthy quality of MJ that an expressed preference strength can'texceed the range of the ballot...? What method could we even compare? Kevin