[EM] Re: Some hard example for Approval Voting

[Rob LeGrand]

Jobst wrote:
> Yesterday I wondered whether under Approval Voting there
> would always be some equilibrium of the following kind:
> All voters specify "sincere" approvals in the sense that when
> they prefer X to Y they do not approve of Y without approving of
> X; and no group of voters can improve their result by changing
> their specified approvals to some different but still "sincere"
> (!) set of approvals.
>
> I hoped that such weak kinds of equilibria might exist always.
>
> Unfortunately, I get the impression that in the following example
> there is no such equilibrium:
>
> 3 D>C>A>B
> 3 D>A>B>C
> 5 A>B>C>D
> 4 C>B>D>A
>
> So, can anybody forecast what will happen with these preferences
> under Approval Voting??

Interesting example.  Bucklin gives B, IRV gives D, Borda gives A
and most methods popular here (beatpath, River, Ranked Pairs) give
C.  There is no Condorcet winner, so there is no Approval
equilibrium; any leader will be quickly toppled if everyone uses
strategy A (which is always sincere in the sense you give above).
Strategy A allows individual voters to move the current result in
the most advantageous direction with no notion of being part of a
new majority coalition; new coalitions emerge naturally from the
smart strategic moves.  Declared Strategy Voting in ballot-by-
ballot mode running for many rounds using Approval and strategy A
elects them with approximate probabilities A 25.05%, B 12.99%, C
27.54% and D 34.42%.

Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/


		
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