2012/2/2 Kevin Venzke <[email protected]> > Hi Jameson, > > *De :* Jameson Quinn <[email protected]> > *À :* Kevin Venzke <[email protected]> > *Cc :* em <[email protected]> > *Envoyé le :* Jeudi 2 février 2012 11h35 > > *Objet :* Re: [EM] SODA criteria > > > > > > > In > your criteria list you had "Majority" but for that you must actually be > assuming the opposite of what I am trying, namely that > *everyone* is delegating, is that right? > > > Everyone who votes for the majority candidate is either delegating to > them, or voting them above all other alternatives - that is, approving only > them but checking "do not delegate". This is the standard meaning of the > majority criterion. For instance, by this meaning, approval meets the > majority criterion. > > For MMC, everyone in the mutual majority is either delegating to one of > the candidates, or approving all of them and nobody else. > > > Oh, I missed that the voter can't rank at all. So you are good with FBC. > But I don't regard Approval as satisfying what I > call MF and Woodall's Majority. It's possible to say it satisfies MF, but > I prefer Woodall's treatment. > > > I don't know what MF stands for. I agree that it fails Woodall's majority, > though not in the unique strong Nash equilibrium. > > > (The criteria framework > I use doesn't have any way to say that Approval satisfies MMC. You can > equate approval with equal-top, above-bottom, or > call it something external, but I can't say that voters stick to a limited > number of slots. I understand the meaning of "two-slot > MMC" or "voted MMC" but I see these as inferior versions.) > > > "voted", because delegation means there's sometimes effectively more than > two slots. > > > In response to your last line, if the majority set involves more than one > candidate, the delegating voters are never part of it > and are unnecessary in getting one of these candidates elected. (I'm using > your treatment that voters only have two rank > levels.) If you don't agree, I'd like to hear how you are interpreting > MMC, because I can't think of how else it would work. > > > 10: A(>B>C>?...) > 10: B(>C>A>?...) > 10: C(>A>B>?...) > 21: ABC > 49: ???? > > One of A, B, or C must win. > > > MF is Majority Favorite. > > If I understand you correctly, you're treating voters as casting either an > approval ballot, or else one of the predeclared > preference orders. >
Yes. I guess that makes sense though it's quite tricky to analyze. If a voter > is counted as voting A>B>C, it's > not possible to raise C above only B. But when I analyze this, it has to > result in something consistent with the desired ranking > unless that's completely impossible. I guess that could only be A, AC, or > ACB approval ballots. I think that would result in > some criteria problems. For instance, suppose that A>B>C elects C, but > A=C=B elects B. Since I look at how the voter > wanted to rank, and not the options the method made available, I would > call that a Mono-raise failure. > I guess I'd have to agree with that... well, if your vote for A=C causes C to lose. So failing participation in this way – for which I recently posted an example scenario, impossible with 4 candidates but possible with 5 – means failing mono-raise. My claim of monotonicity was based on comparing only approval ballots to approval ballots, delegation preferences to delegation preferences, and undelegated bullet votes to delegated votes. I did not consider this case. > You might think that's unfair, but I don't know what framework you can > suggest that will be more apparent and also allow > you to fairly evaluate something like Mono-raise. > Well, you could do as I had done, and evaluate it when the candidate A changes from B>C to B=C. > Personally I think it would be easier to assume voters have no idea what > candidates predeclare. In that case MMC doesn't > apply in your scenario above. > Easier, but I think less realistic. At that point, it's basically approval. > > Granted, this might make it hard for criteria that are supposed to deal > with optimal strategy assumptions or equilibrium. > I just don't worry about those criteria because I don't know how to > evaluate them. > > I also wanted to note, here instead of in a separate post, that I wonder > about the FBC. I was thinking it must satisfy > it because you could cast an approval ballot, but that's not good > reasoning (see: any Condorcet method). What if it > is possible to get a superior result by delegating your vote to someone > other than your favorite? It's not clear to me > that this is impossible. > Say your favorite is W, but you delegate to some other X. They add approvals Y and Z, so that your ballot is counted for X, Y, and Z; and Z wins. You could have just voted for W, X, Y, and Z for the same result. Your approval vote for X gives them the same boost in the delegation order that a delegated vote would have given them. In fact, if you don't like Y, you can probably leave them off. Jameson > > Kevin > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >
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