[EM] Favorite Betrayal and Condorcet

[Kristofer Munsterhjelm]

On 18.04.2022 02:21, Forest Simmons wrote:
> It is well known that Range Voting, no matter its level of resolution,
> is strategically equivalent to Approval. In particular, this means that
> under perfect information conditions there always exists an optimal
> strategy that makes no use of any intermediate ratings. [However, as in
> Linear Programming, existence of an optimal "corner" solution in no way
> denies the possible existence of other equally optimal non-corner
> solutions.]
> 
> Not so well known, but equally true, is that every Condorcet compliant,
> Universal Domain (i.e. RCV) method reduces to  Approval when voters vote
> only at the extremes.
> 
> Question 1. Does every perfect information UD Condorcet election have an
> optimal strategy that makes no use of the intermediate rankings? This
> certainly seems to be the tacit assumption of many Designated Strategy
> Voting methods.

As I understand it, in proper Condorcet methods, it's sometimes useful
to use intermediate rankings because you can both express a preference
for A over B and one for B over C at the same time.

There are modifications of Condorcet that pass the FBC, e.g. Kevin's ICA
and Mike Ossipoff's ICT and Symmetrical ICT. These work by making
Approval strategy equally-optimal so that if (for the purpose of
contradiction) your favorite is F and compromise is C, then F=C>... can
be no worse then C>... But in so doing, they lose Condorcet efficiency.[1]

Kevin's simulations of
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-June/114476.html
seem to indicate that Condorcet methods (at least "advanced" ones like
Schulze) have a low rate of FBC failure. The "Improved Condorcet"
methods would presumably be the flipside of this coin, passing FBC
absolutely but having some (low?) rate of Condorcet failure.

I also seem to recall that MMPO doesn't reduce to Approval despite
passing FBC, but my memory is not the clearest, so I could be mistaken.

-km

[1] A similar trick applied to Borda is Mike's Summed Ranks method.