[EM] SODA criteria
jameson.quinn at gmail.com
Thu Feb 2 10:44:38 PST 2012
2012/2/2 Kevin Venzke <stepjak at yahoo.fr>
> Hi Jameson,
> *De :* Jameson Quinn <jameson.quinn at gmail.com>
> *À :* Kevin Venzke <stepjak at yahoo.fr>
> *Cc :* em <election-methods at electorama.com>
> *Envoyé le :* Jeudi 2 février 2012 11h35
> *Objet :* Re: [EM] SODA criteria
> 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.
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.
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