Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion [?]
On 06/08/2013 10:16 PM, Chris Benham wrote:
Yes.
Say there are three candidates: Right, Centre-Right and Left, and the
approval votes cast are
49: Right
21: Centre-Right (all prefer Right to Left)
23: Left
07: Left, Centre-Right (sincere favourite is Left)
Approval votes: Right 49, Left 30, Centre-Right 28.
The top-2 runoff is between Right and Left and Right wins
70-30.
All the voters who approved Left prefer Centre-Right to Right. The 7
voters who approved both Left and Centre-Right can change the winner to
Centre-Right by dumping Left (their sincere favourite) in the first
round.
49: Right
28: Centre-Right
23: Left
Now the top-2 runoff is between Right and Centre-Right and Centre-Right
wins 51-49.
Seven voters have succeeded with a Compromise strategy.
It seems that this could be generalized to any top-two runoff method.
Consider a base method X, that picks two candidates for the runoff.
Then, even if X passes the FBC, if the situation is so that:
- Candidates A and B go to the runoff if voting is honest,
- some voters that have sincere preferences ACB can replace A with C
by favorite-betrayal,
- in an {A,B} runoff, B will win; in a {B, C} runoff, C will win,
then there's an incentive for favorite betrayal. To completely protect
against that, a method would have to pass a criterion where voters who
prefer C to the honest runoff winner B can't replace either of the
candidates by betraying their favorite (who might not be C). Call this
passing double FBC. But I don't see how a method could possibly do that.
Does that mean that we can't have both FBC and LIIA? The argument would
go in this vein:
- assume X passes both FBC and LIIA, and that the same set of votes are
used for both rounds.
- then the winner in round 2 is the winner in round 1, by LIIA.
- This means that we don't need to consider the runoff as such, only the
base method X.
- And by FBC, for any strategy that involves favorite betrayal, there's
another, non-favorite-betraying strategy that also works.
- So the runoff, being equivalent to just running base method X under
the assumptions given, should pass the FBC.
- But it can't, by the argument above.
- Hence having both FBC and LIIA is impossible.
But something is strange here. Approval is said to pass both FBC and IIA
(which is a superset of LIIA). So where's the flaw?
Thinking a bit further, it seems the flaw is in that the votes don't
change. In the example above, if the runoff is Centre-Right vs. Right,
the 21 CR R L voters aren't going to approve both Centre-Right and
Right in the second round. Since Approval ballots are binary, it's
impossible to express a rank preference over more than two levels, and
so the assumption only holds if the voters' preferences are inherently
dichotomous (in which case the voters who approved of both runoff
candidates would just stay home on the second round).
The argument would still seem to hold for ranked voting, however - at
least if you include the assumptions that voters who vote A = B C
would vote A = B in the runoff. To make the impossibility proof
formal, one would just have to show that no ranked method can pass
double FBC.
-
Finally, I'd like to say that I do understand that reality is a lot less
neat. What Abd says about differences in turnout in the first and second
rounds of a runoff means that criteria are not as useful as for
single-round methods because the votes in the different rounds would
change.
One could even argue that if they don't, there's no reason to add a
runoff to an advanced method, and the only reason for Plurality to have
a runoff is to patch problems in Plurality itself. I have seen reasoning
of this sort from some IRV advocates who both say top-two runoff is
also nonmonotonic, so don't go around saying TTR is better than IRV and
IRV is better than TTR in every way because it's clearly better than
the contingent vote.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion [?]
At 02:46 AM 6/13/2013, Kristofer Munsterhjelm wrote: Finally, I'd like to say that I do understand that reality is a lot less neat. What Abd says about differences in turnout in the first and second rounds of a runoff means that criteria are not as useful as for single-round methods because the votes in the different rounds would change. One could even argue that if they don't, there's no reason to add a runoff to an advanced method, and the only reason for Plurality to have a runoff is to patch problems in Plurality itself. I have seen reasoning of this sort from some IRV advocates who both say top-two runoff is also nonmonotonic, so don't go around saying TTR is better than IRV and IRV is better than TTR in every way because it's clearly better than the contingent vote. IRV advocates, in general, do not value an actual majority choice, and have left centuries of democratic traditions entirely behind. Plurality in nonpartisan elections is based, my suspicion, on a *simulation*. That is, the leader with a plurality will *usually* go on to win a repeated election seeking a majority, and if not being the best, is at least the second best, perhaps good enough. Partisan elections are then based on an expectation that most people will be divided into two major parties. Voting systems activists have, in general, demonized Plurality, when it, *in context and usually* works much better than might be expected. However, it has obvious breakdowns when there is a three-party system and partisan elections. We know this about runoff voting: the election is a comeback election about a third of the time. I base this on a FairVote study. What should actually be done, I don't recall if they did it, is to look at the *margins* in those elections. IRV, *in nonpartisan elections*, almost never is a comeback election, and the exception I saw was with a *very close* margin. I don't recall clearly, but there might have been an additional example, which was an election where the ethnic identity of the candidate was clear from the name, and thus this was a *different kind* of *partisan* election. Ethnically partisan. (For those who don't know, a partisan election permits party affiliation of the candidates to be on the ballot. Voters may thus choose candidates based on that, which is a more stable preference, and more predictable, having little or nothing to do with the candidates themselves. I.e., we might assume that a Green Voter, in an IRV election, might then rank the Democrat second. The problem in Burlington was that the wider second choice was *eliminated* before the Republican, and many Republicans did rank the Democrat second, because the alternative was the Progressive candidate. Hence Bucklin, in that case, could easily have elected the Democrat *with a majority.* Someone tell Burlington that they can have their majority, probably, they do not need to be content with 40%, and their present system can do quite the same thing as IRV. It didn't in the last election, back to TTR/40%, because no Progressive candidate ran! FairVote has been strangely silent.) IRV activists generally will not mention that TTR produces different results than IRV. However, they hint at it by claiming that runoff elections are less representative, completely ignoring that many runoffs are held with the general election. Further, less representative results are commonly accepted in democratic organizations, as long as every qualified voter had the right to vote. They are *not* worse choices, in general. Rather, those who vote represent those who care enough to vote -- it's an effort! -- and thus results are probably *more generally acceptable.* When a *major choice* is presented in a runoff election, people turn out to vote in droves, even if it's a special election. Lizard vs. Wizard, and a similar French election, a boring centrist vs a right-wing extremist. This is the problem with FBC: it is interpreted *strictly*. I.e, *if there is any possible scenario where a voter might have an incentive to betray the favorite, and no matter how small the incentive, the method fails, the criterion becomes functionally useless. There are methods which obviously and routinely fail FBC. There are methods which don't, period, or at least no scenario has been proposed. Now, Range does not fail FBC. However, Range has a problem. It can declare a winner when the majority of voters oppose that result. By the nature of range, that opposition is not at full strength, obviously, but it is a *lack of consent* to the result. Further, because of normalization error, the Range result, even with votes considered fully sincere, can fail to be *actual utility optimizing.* Hence, Smith found that Top-Two runoff Range had better BR results than ordinary Range, with voters who vote with ordinary strategy. I.e, they normalize. They might also bullet vote or expand ranges, but, in
[EM] Does Top Two Approval fail the Favorite Betrayal Criterion [?]
Yes. Say there are three candidates: Right, Centre-Right and Left, and the approval votes cast are 49: Right 21: Centre-Right (all prefer Right to Left) 23: Left 07: Left, Centre-Right (sincere favourite is Left) Approval votes: Right 49, Left 30, Centre-Right 28. The top-2 runoff is between Right and Left and Right wins 70-30. All the voters who approved Left prefer Centre-Right to Right. The 7 voters who approved both Left and Centre-Right can change the winner to Centre-Right by dumping Left (their sincere favourite) in the first round. 49: Right 28: Centre-Right 23: Left Now the top-2 runoff is between Right and Centre-Right and Centre-Right wins 51-49. Seven voters have succeeded with a Compromise strategy. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion [?]
Thanks to Chris for attempting this. This is a partisan election, apparently, which is an issue in terms of whether or not scenarios are realistic. But I'll set that aside for the moment. At 03:16 PM 6/8/2013, Chris Benham wrote: Yes. Say there are three candidates: Right, Centre-Right and Left, and the approval votes cast are 49: Right 21: Centre-Right (all prefer Right to Left) 23: Left 07: Left, Centre-Right (sincere favourite is Left) It's really irritating that Center is misspelled, and favorite, too. :-) Okay, this is an election where Left is no-hope. The winner is going to come, with a sane method, from Right or Centre-Right. 51% of voters prefer Centre-Right to Right, reasonable compromise. The votes are reasonable, except that 23 Left bullet voters are unreasonable, in fact. I'd assume they know their position. Not too unreasonable, though. After all, Left is in second place as to first preferences. This is a center squeeze election. Approval votes: Right 49, Left 30, Centre-Right 28. The top-2 runoff is between Right and Left and Right wins 70-30. I've generally pointed to the problem of assuming the same electorate for runoffs, but let's, again, leave that aside. This is reasonable. What is somewhat unreasonable about this scenario is the Right bullet voters. It is *very strange* that none of them also approve Centre-Right. All the voters who approved Left prefer Centre-Right to Right. The 7 voters who approved both Left and Centre-Right can change the winner to Centre-Right by dumping Left (their sincere favourite) in the first round. 49: Right 28: Centre-Right 23: Left Now the top-2 runoff is between Right and Centre-Right and Centre-Right wins 51-49. Seven voters have succeeded with a Compromise strategy. Looks correct to me. They can do that. The strategy works, in fact, because Centre-Right is the best winner, though only by a small margin. The strategy is *necessary* because of the 23 Left voters who don't approve of Centre-Right. But there is something else going on here. In a real runoff election, those 23 Left bullet voters are not likely to show up to vote. Motivating them will be difficult. Remember that they didn't vote for Centre-Right in the primary; this represents low preference strength between R and CR. Why will they suddenly have high enough preference strength to show up and vote? In the U.S., that is. If the turnout of those original Left voters is even slightly depressed, Right will win the runoff. Right has high preference strength, that's shown by the lack of additional approvals for Centre-Right. I think the strategy could easily fail. Would *probably* fail. The low Left vote count in the primary would damage the Left party. They might *possibly* get a better result from this election, but the next, they are dead. Left will become increasingly irrelevant. I agree that the example shows FBC violation on the face, and thank Chris for this example. I also see that this example is (1) implausible, ultimately, and (2) would not lead to voter backlash. I.e., the Left voters would vote as they voted, and the Left voters would be kicking themselves for not voting for Center-Right, those that didn't, not for *failing* to betray their favourite. The problem that led to Right winning was not that they voted for their Favourite, but that they failed to vote for second-best, leaving that to the runoff. Just barely, they got their favourite into the runoff, wasting everyone's time, and their own campaign funds. Approval has this problem, we know that. To fix it, Bucklin. Let's take the same apparent voting strengths 49: Right translates to 40: R 9: R,-,CR 21: Centre-Right (all prefer Right to Left) translates to 21: CR,-,R 23: Left translates to 15: L 8: L,-,CR 07: Left, Centre-Right (sincere favourite is Left) translates to 7: L,CR I just guessed at some voting patterns, I did not tweak them to produce a desired result. In real Bucklin elections, we saw *lots* of additional preferences added. I assumed the voters here are sophisticated enough to know that skipping middle rank expresses higher preference strength, that third rank is *minimal approval*. 1st rank: 49: R 21: CR 30: L shows sincere first preferences. That's an advantage in itself. A strategy might win, but has other costs. 2nd rank pulled in 49: R 28: CR 30: L both L and R are failing to get additional preferences. 3rd rank pulled in 70: R 73: CR 30: L Either CR wins or there is a runoff between R and CR, so the L voters do not need to betray their favorite. I used all the preferences mentioned, but I added some level of delayed second-choice for the R voters. That's not necessary. If those voters continued to bullet vote, the result would be the same with a mandatory runoff. What makes the election work with Bucklin is the addition of second preferences for supporters of a no-hope candidate. The only reason the 7 voters
Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion
At 10:51 AM 6/7/2013, Jameson Quinn wrote: I'm sorry, I don't want to get into an interminable back and forth with someone who misuses my name and doesn't apologize, and prefers you didn't prove it! to working anything out for themselves or asking nicely for evidence. Jameson, I responded substantially and in detail to your claim of FBC failure. You are not obligated to respond to anything. You showed nothing, not even a weak evidence, beyond the name turkey-raising, just a claim. And if you are content with that, that's your privilege. For me, and so far, unless someone comes up with a plausible scenario, it stands as demonstrated that a claim of FBC failure for top-two runoff, based on a turkey-raising strategy, is meaningless. Turkey-raising, under Approval/runoff, does not establish FBC failure, because one could still vote for the Favorite without harming the strategy. As we will see more proposed usage of approval and approval methods with runoff voting, it's an important issue. Who misused your name? What are you talking about? What is to apologize for? It's not nice to point out that a point has not been supported? What? (no more original content below.) JamesON 2013/6/7 Abd ul-Rahman Lomax mailto:a...@lomaxdesign.coma...@lomaxdesign.com At 06:28 PM 6/6/2013, Jameson Quinn wrote: 2013/6/6 Abd ul-Rahman Lomax mailto:a...@lomaxdesign.coma...@lomaxdesign.com Subject was: Re: [EM] Someone thinks that Approval should meet the Mutual Majority Criterion James does not help us out with a description of why it fails. Should I start calling you Joe now? :) You may join any club that will admit you. Ask Michael. Others have said how it fails: through a turkey-raising strategy. Implausible, unlikely, as you may have it; but still clearly possible. Actually, that was not said recently. It's not only implausible, it does not appear to violate FBC. That is why I have asked for specifics. Favorite Betrayal Criterion: Wikipedia: A http://en.wikipedia.org/wiki/Voting_systemhttp://en.wikipedia.org/wiki/Voting_systemvoting system satisfies the Favorite Betrayal Criterion (FBC) if there do not exist situations where a voter is only able to obtain a more preferred outcome (i.e. the election of a candidate that he or she prefers to the current winner) by insincerely listing another candidate ahead of his or her sincere favorite.http://en.wikipedia.org/wiki/Favorite_betrayal_criterion#cite_note-1http://en.wikipedia.org/wiki/Favorite_betrayal_criterion#cite_note-1[1] Scorevoting.net (article by Ossipoff and Smith): Voters should have no incentive to vote someone else over their favorite. After my usual carping about absolute standards like no incentive -- Space Aliens can provide strong incentives -- I don't see how a turkey-raising strategy with an Approval primary involves betrayal of the Favorite. It does involve betrayal of a lower preference. I.e., primary unconditionally feeds top two to runoff, which is vote-for-one. I.e., this is the Arizona system, without the Approval feature. Voter prefers ABC. Voter fears that if runoff is A vs. B, B could win, so votes for C. This voter is going to wet his or her pants if C leads, but, never mind, maybe in the runoff A will win, because these turkey farmers are not going to vote for C in the runff. But, now suppose this is an Approval primary, i.e, this is in Arizona and it's a municipality that's implemented the system. Never mind that turkey raising is something that turkey farmers in Arizona would never admit to. Out in the Arizona desert, folks get along, and are straightforward and honest with each other. But, just suppose they try this. Okay, how does it show up? They could vote for C, hoping to push B out of the runoff. They actually can't do that, because of write-ins, which are allowed, but, hey, they can dream, they could even dream of Space Aliens telling them to vote this way. In fact, given that this is Arizona, that's fairly plausible. Something about the cloud formations. No, wait, that's New Mexico. But a little detail about FBC. Sure, they could vote for C, but if what they want is for A to win, which is the whole motivation for running this devious plan, why don't they also vote for A? They are pushing for B to be excluded, and, this way, they push with two candidates (or more). from the Smith-Ossipoff page: one can prove FBC-compliance by the following strategy: If betraying favorite F in order to make X win is the plan, and if that plan actually works, then the alternate non-betrayal plan of simply raising X to be co-equal top with F (carried out by the same set of voters who planned to betray F, using the same set of votes they planned on) also works to make X win. Q.E.D. There is no incentive to vote C above A, the favorite. Want to raise the turkey, C, to exclude B? Fine. Also vote for A. No Betrayal. Indeed, this is part of a more sophisticated
Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion
Let's just drop this. You're technically wrong but substantially right, and I don't see what's to be gained by convincing you of that that's worth the time I think it would take. As to the name thing, you called me James. No big deal, really. I made the Joe joke, then you didn't realize what I was talking about and implied I was serious. Misunderstanding. Cheers, Jameson 2013/6/7 Abd ul-Rahman Lomax a...@lomaxdesign.com At 10:51 AM 6/7/2013, Jameson Quinn wrote: I'm sorry, I don't want to get into an interminable back and forth with someone who misuses my name and doesn't apologize, and prefers you didn't prove it! to working anything out for themselves or asking nicely for evidence. Jameson, I responded substantially and in detail to your claim of FBC failure. You are not obligated to respond to anything. You showed nothing, not even a weak evidence, beyond the name turkey-raising, just a claim. And if you are content with that, that's your privilege. For me, and so far, unless someone comes up with a plausible scenario, it stands as demonstrated that a claim of FBC failure for top-two runoff, based on a turkey-raising strategy, is meaningless. Turkey-raising, under Approval/runoff, does not establish FBC failure, because one could still vote for the Favorite without harming the strategy. As we will see more proposed usage of approval and approval methods with runoff voting, it's an important issue. Who misused your name? What are you talking about? What is to apologize for? It's not nice to point out that a point has not been supported? What? (no more original content below.) JamesON 2013/6/7 Abd ul-Rahman Lomax mailto:a...@lomaxdesign.coma** b...@lomaxdesign.com a...@lomaxdesign.com At 06:28 PM 6/6/2013, Jameson Quinn wrote: 2013/6/6 Abd ul-Rahman Lomax mailto:a...@lomaxdesign.coma** b...@lomaxdesign.com a...@lomaxdesign.com Subject was: Re: [EM] Someone thinks that Approval should meet the Mutual Majority Criterion James does not help us out with a description of why it fails. Should I start calling you Joe now? :) You may join any club that will admit you. Ask Michael. Others have said how it fails: through a turkey-raising strategy. Implausible, unlikely, as you may have it; but still clearly possible. Actually, that was not said recently. It's not only implausible, it does not appear to violate FBC. That is why I have asked for specifics. Favorite Betrayal Criterion: Wikipedia: A http://en.wikipedia.org/**wiki/Voting_systemhttp://en.wikipedia.org/wiki/Voting_system http://en.**wikipedia.org/wiki/Voting_**systemhttp://en.wikipedia.org/wiki/Voting_systemvoting system satisfies the Favorite Betrayal Criterion (FBC) if there do not exist situations where a voter is only able to obtain a more preferred outcome (i.e. the election of a candidate that he or she prefers to the current winner) by insincerely listing another candidate ahead of his or her sincere favorite.http://en.**wikipedia.org/wiki/Favorite_** betrayal_criterion#cite_note-1http://en.wikipedia.org/wiki/Favorite_betrayal_criterion#cite_note-1 **http://en.wikipedia.org/wiki/**Favorite_betrayal_criterion#** cite_note-1http://en.wikipedia.org/wiki/Favorite_betrayal_criterion#cite_note-1[1] Scorevoting.net (article by Ossipoff and Smith): Voters should have no incentive to vote someone else over their favorite. After my usual carping about absolute standards like no incentive -- Space Aliens can provide strong incentives -- I don't see how a turkey-raising strategy with an Approval primary involves betrayal of the Favorite. It does involve betrayal of a lower preference. I.e., primary unconditionally feeds top two to runoff, which is vote-for-one. I.e., this is the Arizona system, without the Approval feature. Voter prefers ABC. Voter fears that if runoff is A vs. B, B could win, so votes for C. This voter is going to wet his or her pants if C leads, but, never mind, maybe in the runoff A will win, because these turkey farmers are not going to vote for C in the runff. But, now suppose this is an Approval primary, i.e, this is in Arizona and it's a municipality that's implemented the system. Never mind that turkey raising is something that turkey farmers in Arizona would never admit to. Out in the Arizona desert, folks get along, and are straightforward and honest with each other. But, just suppose they try this. Okay, how does it show up? They could vote for C, hoping to push B out of the runoff. They actually can't do that, because of write-ins, which are allowed, but, hey, they can dream, they could even dream of Space Aliens telling them to vote this way. In fact, given that this is Arizona, that's fairly plausible. Something about the cloud formations. No, wait, that's New Mexico. But a little detail about FBC. Sure, they could vote for C, but if what they want is for A to win, which is the whole motivation for running this
Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion
At 06:10 PM 6/7/2013, Jameson Quinn wrote: Let's just drop this. You're technically wrong but substantially right, and I don't see what's to be gained by convincing you of that that's worth the time I think it would take. As to the name thing, you called me James. No big deal, really. I made the Joe joke, then you didn't realize what I was talking about and implied I was serious. Misunderstanding. Weird. I actually looked through the mail to find where I might have used the wrong name for you and didn't notice that *it was right there.* But I didn't think you were serious, Jameson. After all, you had a smiley face there. I responded, then, deadpan. How did I imply you were serious? As to the issue, no, I want to know, but it doesn't have to be from you. You are claiming I'm technically wrong, and perhaps I am, but I have not see the evidence. Turkey raising didn't cut it. Once again, anyone, see the question in the subject header. If it fails, please show an example. To repeat, let this be the basic definition of top two approval. Approval voting is used for a primary and the top two candidates are placed on the ballot in the general election. Write-in votes are allowed in the runoff. Does the primary fail FBC? (This is the Arizona proposal, recently referred to a special advisory committee on approval voting, it appears, if the House passes the amended version.) Trick bonus question: if the general election is also approval, does the method fail FBC? Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Does Top Two Approval fail the Favorite Betrayal Criterion
Subject was: Re: [EM] Someone thinks that Approval should meet the Mutual Majority Criterion At 01:56 PM 6/6/2013, Jameson Quinn wrote: 2013/6/6 Abd ul-Rahman Lomax mailto:a...@lomaxdesign.coma...@lomaxdesign.com Another issue that was left a bit hanging in discussions on the CES list: Does top-two Approval fail the Favorite Betrayal Criterion? There are really two forms of top-two Approval to be considered, plus a third detail. 1. Top two approval where two candidates advance to the general election. This fails FBC. I am sympathetic to Abd's arguments about how the electorate will change based on preference strength, and how well-informed voters will tend to find a way to avoid FBC failure, but that doesn't mean that it passes the criterion, merely that the failure is minor. James does not help us out with a description of why it fails. Further, failure is minor is an issue when using voting systems criteria to study voting systems. That's the problem with using the criteria as absolutes. I did not give examples because I'm not asserting failure. Someone who is asserting it, I'd prefer that they at least show an example. It would be generous to cover the underlying utilities motivating the behavior, but I'll do that if the writer doesn't. (Or will infer them and might show that they do not significantly motivate the behavior, as a rough and nonspecific analysis is telling me.) 2. Top two approval where a candidate with a majority can win, otherwise two candidates advance. Still fails, although it's slightly better. From what point of view? *How* is it better? *How much* better? 3. If write-in votes are allowed in the runoff, the primary is actually a nomination device, not the actual election. The actual election being Approval, the combination must satisfy FBC if Approval does, and it does. This is true... but only if there's a hard threshold for making it to the second round. That is, all candidates with over 1/3 approval advance, or some such; and if there are fewer than 2 such candidates, the highest approval wins in the first round. No. Threshold has nothing to do with it. If the primary is only a nomination device, it is like petition requirements or partisan primaries. Understand that this is like the Arizona proposal, but with Approval in the final election. If the final election is Approval, Approval satisfies FBC, because the voters may still vote for their Favorite in the general election. There is no cost to that, and by the rule that a method satisfies FBC if there is a simple way for the voter to actually vote for their Favorite and not betray the Favorite by voting for someone else *over* the Favorite, and gain as good an expected result, then FBC is satisfied. (If write-in votes are allowed, in this concept, the runoff must also be Approval.) Arizona had a method up for legislative passage that would have allowed municipalities to use a two-stage voting system with an Approval primary, top-two advancing to the general election with ballot placement, and, apparently, write-ins allowed in the general election (as well as in the primary). The primary has no majority test, it is top-two plurality, but voters may vote for as many candidates as they choose. The runoff is standard vote-for-one. So, first of all, does this method fail FBC? If so, is the scenario plausible for real voters? These are nonpartisan elections. I'm not seeing any actual analysis here, just authoritarian statements. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion
2013/6/6 Abd ul-Rahman Lomax a...@lomaxdesign.com Subject was: Re: [EM] Someone thinks that Approval should meet the Mutual Majority Criterion At 01:56 PM 6/6/2013, Jameson Quinn wrote: 2013/6/6 Abd ul-Rahman Lomax mailto:a...@lomaxdesign.coma** b...@lomaxdesign.com a...@lomaxdesign.com Another issue that was left a bit hanging in discussions on the CES list: Does top-two Approval fail the Favorite Betrayal Criterion? There are really two forms of top-two Approval to be considered, plus a third detail. 1. Top two approval where two candidates advance to the general election. This fails FBC. I am sympathetic to Abd's arguments about how the electorate will change based on preference strength, and how well-informed voters will tend to find a way to avoid FBC failure, but that doesn't mean that it passes the criterion, merely that the failure is minor. James does not help us out with a description of why it fails. Should I start calling you Joe now? :) Others have said how it fails: through a turkey-raising strategy. Implausible, unlikely, as you may have it; but still clearly possible. Further, failure is minor is an issue when using voting systems criteria to study voting systems. That's the problem with using the criteria as absolutes. Yes, it's an issue. Absolutely. The difference between failing badly and barely failing, is often larger than the difference between barely failing and passing. But that doesn't mean you shouldn't be clear about the difference. I did not give examples because I'm not asserting failure. Someone who is asserting it, I'd prefer that they at least show an example. It would be generous to cover the underlying utilities motivating the behavior, but I'll do that if the writer doesn't. (Or will infer them and might show that they do not significantly motivate the behavior, as a rough and nonspecific analysis is telling me.) 2. Top two approval where a candidate with a majority can win, otherwise two candidates advance. Still fails, although it's slightly better. From what point of view? *How* is it better? *How much* better? If any candidate has a majority, there is no FBC failure. If not, you have system 1, which can fail FBC as explained above. Since that is only part of the time, it is only partly as bad. 3. If write-in votes are allowed in the runoff, the primary is actually a nomination device, not the actual election. The actual election being Approval, the combination must satisfy FBC if Approval does, and it does. This is true... but only if there's a hard threshold for making it to the second round. That is, all candidates with over 1/3 approval advance, or some such; and if there are fewer than 2 such candidates, the highest approval wins in the first round. No. Threshold has nothing to do with it. If the primary is only a nomination device, it is like petition requirements or partisan primaries. Understand that this is like the Arizona proposal, but with Approval in the final election. If the final election is Approval, Approval satisfies FBC, because the voters may still vote for their Favorite in the general election. There is no cost to that, and by the rule that a method satisfies FBC if there is a simple way for the voter to actually vote for their Favorite and not betray the Favorite by voting for someone else *over* the Favorite, and gain as good an expected result, then FBC is satisfied. If the primary is not considered as part of the election process, then sure, it could consist of shooting any candidate with an even number of votes, and it would not cause FBC failure. But if you are considering it as part of the election, you can't just make it up as you go along. A hard threshold, or a threshold based on a mathematical function of the top candidate's votes alone, causes no FBC failure. A set number of candidates advancing causes FBC failure, though not a particularly serious one. (If write-in votes are allowed, in this concept, the runoff must also be Approval.) Arizona had a method up for legislative passage that would have allowed municipalities to use a two-stage voting system with an Approval primary, top-two advancing to the general election with ballot placement, and, apparently, write-ins allowed in the general election (as well as in the primary). The primary has no majority test, it is top-two plurality, but voters may vote for as many candidates as they choose. The runoff is standard vote-for-one. So, first of all, does this method fail FBC? If so, is the scenario plausible for real voters? These are nonpartisan elections. I'm not seeing any actual analysis here, just authoritarian statements. So? Right and wrong are not decided by word counts or votes. Jameson Election-Methods mailing list - see http://electorama.com/em for list info
