[EM] IRV Participation clarification
EM list-- When I said that someone who decides to show up vote, in an IRV (Alternative Vote) election, can make his last choice win thereby, when that wouldn't have happened had that voter stayed home, I mean that that can happen even if the voter votes sincerely. IRV fails Participation as you Steve defined it. But of course that's the least of IRV's failings. Would you believe that there's actually an organization that's heavily promoting that the piece of crap that it calls IRV? Sometimes it seems that we're being lax because we aren't out telling people what we know about the problems of methods that are being offered to the public. People have a right to know. Don't we have a responsibility to tell them? Mike Ossipoff Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com
Re: [EM] Participation SARC
Dear Steve,
you wrote (5 May 2000):
The wording of the participation criterion by Herve Moulin
(Axioms of Cooperative Decision Making, Cambridge University
Press, 1988, p.239) refers to a single voter, not a group:
Participation: Say that candidate a is elected from the set A
by the electorate N. Next consider a voter i outside N.
Then the electorate N U {i} should elect a or some candidate
whom agent i strictly prefers to a.
Actually, it doesn't matter whether you are talking about a
single voter or a same-voting group of voters.
1. If a single voter cannot be punished for voting, then also
a same-voting group of voters cannot be punished for voting.
The reason: You can simply take one voter of this group after
the other. If the same-voting group worsened the result of
the elections, then -when you take one voter of this group after
the other- at least one voter of this group would worsen the
result of the elections.
2. If a same-voting group cannot be punished for voting, then
also a single voter cannot be punished. The reason: Every voter
forms a group of one voter.
Therefore, Herve Moulin's definition and my definition of
participation are identical. By the way: In "Condorcet's Principle
Implies the No Show Paradox" (Journal of Economic Theory, vol. 45,
p. 53-64, 1988), Moulin always uses same-voting groups to prove
a violation of participation.
**
You wrote (5 May 2000):
A criterion like SARC seems better than participation when the
voters are sophisticated (and unconstrained by accountability,
e.g., secret ballot), since it is unreasonable to compare only
sincere voting and the abstention strategy when other strategies
may be better than both of those.
The problem is: To be able to compare sophisticated outcomes, you
have to make presumptions about the used strategies. It is not
easy to make non-trivial justifiable realistic presumptions
about the used strategies.
**
You wrote (5 May 2000):
For participation to be considered an important criterion in
large public elections, wouldn't there need to be empirical
evidence that significant numbers of voters will routinely not
vote due to a procedure's failure to rigorously comply with
participation? (Voter turnout might actually increase overall,
given a procedure which fails participation but does a good job
of solving other problems like spoiling.) Also, is there a
plausible argument that society would be worse off using a
procedure which doesn't rigorously comply with participation?
Supporters of Alternative Voting usually claim that Alternative
Voting guarantees that a set of additional voters each with the
same sincere opinion can never be punished for going to the
polls and voting sincerely. They claim that -as Alternative
Voting guarantees that a vote of a given voter for a given
candidate will never be counted unless all those candidates who
are prefered to this given candidate by this given voter cannot
be elected any more- a voter cannot be punished for making an
additional preference. And they claim that this means that
an additional voter cannot be punished at all for going to
the polls and voting sincerely.
The participation criterion is the mathematical formulation of
the claimed property of Alternative Voting.
Independently on whether you think that a given property is
important, you have to find a mathematical formulation of this
property to be able to discuss it in a non-trivial manner.
**
You wrote (5 May 2000):
I haven't seen any messages posted by Lucien in years. Is it
correct to use the present tense when describing his advocacy?
Lucien Saumur still promotes Smith//RandomCandidate.
Markus Schulze
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Re: [EM] Participation SARC
Steve had said: A criterion like SARC seems better than participation when the voters are sophisticated (and unconstrained by accountability, e.g., secret ballot), since it is unreasonable to compare only sincere voting and the abstention strategy when other strategies may be better than both of those. Markus said: The problem is: To be able to compare sophisticated outcomes, you have to make presumptions about the used strategies. It is not easy to make non-trivial justifiable realistic presumptions about the used strategies. I reply: Presumptions? Voters' common use of defensive order-reversal in Plurality isn't a presumption--it's a well-known fact. In general, it's surely a safe presumption that voters will vote to gain the best outcome that they can, based on some way in which they feel sure that other voters will vote. Or that they'll vote so as to maximize their expectation, based on their valuations of the candidates the relevant probabilities. Voting behavior when Plurality is used is best explained by those presumptions. Those are justifiable realistic presumptions. Non-trivial? I'm not sure what that means here, but if you mean that justifiable realistic presumptions can only be made under special rare conditions, that isn't correct. ** Steve had said: You wrote (5 May 2000): For participation to be considered an important criterion in large public elections, wouldn't there need to be empirical evidence that significant numbers of voters will routinely not vote due to a procedure's failure to rigorously comply with participation? (Voter turnout might actually increase overall, given a procedure which fails participation but does a good job of solving other problems like spoiling.) Also, is there a plausible argument that society would be worse off using a procedure which doesn't rigorously comply with participation? Markus said: Supporters of Alternative Voting usually claim that Alternative Voting guarantees that a set of additional voters each with the same sincere opinion can never be punished for going to the polls and voting sincerely. They claim that -as Alternative Voting guarantees that a vote of a given voter for a given candidate will never be counted unless all those candidates who are prefered to this given candidate by this given voter cannot be elected any more- a voter cannot be punished for making an additional preference. And they claim that this means that an additional voter cannot be punished at all for going to the polls and voting sincerely. I reply: Yes, and that familiar IRVie claim for the Alternative Vote (currently promoted under the name "IRV") is false. Even in simple, plausible, 3-candidate examples, voters in IRV can cause their last choice to win, because they voted, when that wouldn't have happened had they not voted. Markus said: The participation criterion is the mathematical formulation of the claimed property of Alternative Voting. I reply: IRV fails that criterion. But for IRV to fail a criterion isn't unusual; it fails much more important ones than Participation. Markus said: Independently on whether you think that a given property is important, you have to find a mathematical formulation of this property to be able to discuss it in a non-trivial manner. Excuse me, Markus, but what mathematical formulation is lacking in SARC? And will you please tell me what "non-trivial" means? Or maybe the way to word this question is: What is it about SARC that makes you say that it lacks a mathematical formulation that a criterion should have? And if you feel that some of my other criteria lack a necessary mathematical formulation, would you specify what it is about them that would make you say that they lack a mathematical formulation that a criterion should have. One thing I admit is that I still haven't put an extended "voting equilibrium" (extended to non-point systems) on a precise basis. So of course I can't write a precise criterion that speaks of that equilibrium. But I'd be interested in what you'd say that my other criteria lack, that a criterion needs. If you mean that all criteria have to be written in the stilted symbolic jargon found in some journal articles, then I'd ask who says criteria need that, and how would you show that they need that. If it's because spoken language can be ambiguous at times, I believe that it's possible to write something in ordinary language (as opposed to symbols borrowed from mathematics) in a way so that people know what it means. Surely that's the goal of language. And I've noticed that authors who use mathematical symbols still need lots of ordinary language to try to clarify what their symbols mean. Actually, I'd say the opposite: Criteria method definitions that are written only in that symbolic jargon borrowed from mathematics are useless for showing to the people to whom criteria most need to be shown. Mathematicians can exchange symbols forever,
Re: [EM] Probabilistic criteria. Participation no-show.
I've only heard of one person advocating such a method, and he didn't have a proposal, only the suggestion that maybe a good method of that type could someday be found. Markus said-- I guess that you are talking about Albert Langer. But remember e.g. that Lucien Saumur promotes Smith//RandomCandidate. I comment: True. And so it could be of some interest how his method does by criteria generalized to cover random methods. But Smith//RandomCandidate isn't a proposal that we reform advocates are ever going to have to deal with as a competitor or a serious rival, if only because random selection would never be accepted by the public, or by the people who write media articles. It seems to me that RandomBallot did worse in Norman's simulation than any other method. RandomCandidate seems like it would surely do worse. Simulation results like that further clinch the public unacceptability of random methods. I personally don't have much objection to trying such a method, because eventually we'd get lucky and get a good President, and the public might find out that they like his policies. But as a proposal, it's out of the question. ** Markus said: The participation criterion says that the participation in the election by a same-voting group of voters should never worsen (due to the opinion of this group) the result of the elections. Of course, the participation criterion presumes sincere voting because (1) if this additional group of voters votes insincerely then -as we know only the reported opinion and not the sincere opinion of this group- we cannot check whether it worsens the result of the elections due to its sincere opinion. and (2) if I reply: Yes, but, whether we can check it or not, it's still meaningful useful to talk about what they can do to themselves, without assuming sincere voting. Because, whether we can check it or not, people surely will (and do) vote insincerely in Pluality, and surely will in Borda. In fact, as I discussed when I mentioned Myerson-Weber equilibrium, the fact that we can't check on that giveaway is what makes it particularly dangerous, and a bad result that the electorate can get mistakenly stuck in. For instance, using the familiar example of Plurality, the notoriously common insincere voting people do in Plurality , and the obvious incentive for it, makes Plurality fail SARC. Whether the vote-totals reveal it or not, it still is undesirable for someone who prefers Nader to defeat Nader by voting for Gore. So, instead of sincere voting, I prefer to assume only reasonable voting, voting in a way that could conceivably be the voter's best strategy, with some configuration of the other people's votes. Markus continued: And (2): This additional group of voters voted insincerely and worsened the result of the elections due to its sincere opinion then this wouldn't be considered as a problem because this fact would deter this group from voting insincerely. I reply: Of course it's a problem, because, though dumping one's favorite can and often will worsen the voter's result, it regrettably _doesn't_ deter the insincere voting. Voters will give their support away to someone whom they believe they need as a compromise, and routinely dump their favorite in order to do so. And if Nader had a win, but his voters gave it away by voting for Gore, the election count results wouldn't show what happened. Voters wouldn't be deterred from giving the election away again again, because the count results don't show that it happened. The count results will merely show that Gore is a big votegetter, and that very few voted for Nader, confirming what the Nader-to-Gore giveaway voters believed. That's the voting equilibrium that Myerson Weber wrote about. Now, with Approval it would be different, and a giveaway wouldn't escape notice, as I spoke of when I wrote about Myerson's Weber's discussion. Aside from that, Approval will never have the kind of giveaways that happen with Plurality, and will happen with IRV Borda. And, with Approval, voters who vote in a way that could conceivably be their best strategy, as spelled out in SARC, will never defeat their sincere favorite or elect their sincere last choice. Yes, the academics mostly seem to ignore the possibility of defensive order-reversal, and the fact that the need for it creates a problem. By the way, I should add that, under the conditions that authors quoted by Tideman consider plausible and worth considering, something stronger than SARC compliance can be said for Approval: A group of same-voting voters who share the same preferences, and vote in a way that could, with some configuration of the other people's votes, gain an outcome that they like better than all the outcomes that they could get by other ways of voting, will never worsen their result, compared to what it would have been had they not showed up voted. The above is true unless there are improbably inconsistent frontrunner probabilities, a
