[EM] [CES #9416] SODA properties

Jameson Quinn jameson.quinn at gmail.com
Mon Oct 21 20:23:01 PDT 2013

Bruce: yes, you're right, monotonicity is important. Also, I've spent
months thinking about this and I finally have a proof, so I'm certainly not
about to leave it out of my "paper" (since it's just arxiv, not
peer-reviewed, "paper" is a bit generous; but I hope it will fly as a
wikipedia RS).

Beyond that, I'm thinking I want to give a series of three properties that
address my "three-level voting-system challenge". That is, spoilers,
center-squeeze, and chicken dilemma.

For handling spoilers, the property is obvious: [voted] mutual majority.

For handling center squeeze, I'm thinking something like "CUSP": that is,
the Condorcet winner under Universal, Single-peaked Preferences is a
"dominant Nash equilibrium" (a strong Nash equilibrium whose individual
strategies all would be weakly dominant if used unilaterally in any other
Nash equilibria that might exist). Again, it's a mouthful, but it's not
actually a hard property to meet; it holds for most Condorcet, for
Approval, Range, and MAV/(G)MJ/etc. Basically, it's failed by plurality,
IRV, Borda, and most runoff systems.

... Wait a minute. I'm so used to thinking in terms of strategy and Nash
equilibria, that I'm making this too complicated. "CUSP" should be defined
as just, the Condorcet winner wins for any *honestly-voted* 1-D universal
single-peaked preference.

For handling the chicken dilemma, I suspect that the best way to
characterize voting systems will take a page from Bouton and Castanheira,
and see about strategies for voters who aren't entirely sure that their
perceived favorite will give them the highest payoff, and so have a weak
incentive to cooperate in order to use the voting system to find the best
candidate. That would involve some tricky probability calculations, but I
suspect that the result will be that for such a criterion, IRV > SODA > MAV
> (G)MJ > Condorcet > Range > Approval. (IRV does well on this third
hurdle, but having already tripped badly on the first two hurdles, it is
not a contender overall).

2013/10/21 Bruce Gilson <brgster at gmail.com>

> On Mon, Oct 21, 2013 at 7:24 PM, Jameson Quinn <jameson.quinn at gmail.com>wrote:
>> [...]
>> So, given all the above, I think this is actually an outstandingly good
>> system. But... if you only had room to state and prove, say, 3 or 4 of the
>> above properties, which would you focus on?
> Well, given that to me monotonicity is one of the most serious problems in
> IRV, which is being proposed quite actively, that's one of the major ones.
> I'm not going to come up with "3 or 4," but 'm sure you'll get more from
> others in this group.
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