[EM] FBC definitions

[MIKE OSSIPOFF]

Alex--

You wrote:

Probably the most significant difference between my definition and yours
is that you focus on the incentives facing a single voter given all other
voters' ballots, while I focus on the incentives facing a coalition of
like-minded voters (i.e. a set of voters with identical ordinal
preferences, but not necessarily the same cardinal preferences).

I reply:

One difference, the one that I mentioned, is that you say that no one should 
have incentive to vote someone over hir favorite, while, just as you said, I 
say that it shouldn't be possible to contrive a configuration of other 
people's ballots such that a voter can only optimize hir outcome by voting 
someone over hir favorite. Your incentive approach is more demanding, but 
Approval complies with both definitions.

As for defining FBC in terms of sets of voters instead of an individual, I 
don't know how such a definition would go. You're saying that no same-voting 
set of voters should have incentive to vote someone over their (shared) 
favorite?

Sure, an individual voter can only make or break a tie for first place (in 
point systems such as Approval, Plurality, or CR) or a pair-tie( in 
pairwise-count methods such as Condorcet). But doing so can change the final 
single-winner outcome in the voter's favor, when the random tiebreaker is 
applied to a tie (or when  the tie that the voter could have lost never 
happens because he made someone better win instead).

To me, it seems simpler to speak of one voter, and that approach works fine. 
  If you prefer X to Y, an X victory is better for you than an XY tie, and 
an XY tie is worth more to you than a Y victory.

Most criteria say that, under certain premise conditions, something should 
always be true, or something should never happen.  FBC says that a certain 
thing should never be true, and the fact that a failure example requires an 
unlikely situation where your vote can make or break a tie, doesn't make it 
any more difficult to write that failure example.

Defining voting Nash equiilbrium is different, because  no player must be 
able to improve his outcome by voting differently, and if a player is one 
voter, then obviouslyall but the rarest vote configurations are Nash 
equilibria. So on EM we've been saying that a Nash equilibrium is a ballots 
configuration, and the resulting outcome,  in which no set of voters can an 
outcome that they all like better by voting differently.

So, in that case, it's necssary to talk of a set of voters inorder for Nash 
equilibrium to mean what one would expect and be useful for voting.

You could write FBC in terms of a set of voters too, but it isn't necessary. 
On the other hand, there's no reason to object to an FBC definition that is 
about a set of same-voters who share the same favorite. In fact, my FBC 
failure examples have been about a whole set of voters anyway, instead of 
being about one voter, as they should, strictly speaking, to match my FBC 
wording. So I should either change the failure examples that I use, or else 
change my wording to speak of a set of voters instead of one voter.

Mike Ossipoff



The rationale is that if I prefer A>B>C, and you prefer A>B>C, it doesn't
really matter from a STRATEGIC standpoint whether I think A is much better
than B while you think A is just slightly better than B.  All that matters
is that we'd both benefit from a maneuver that elects A instead of B or B
instead of C.  Of course, from a POLITICAL standpoint it could matter a
great deal, but that goes beyond the strategic issues I'm considering at
the moment.

Another rationale for focusing on groups of voters is that in many cases a
single voter can at best change it from a definite result to a tie, while
a coalition of voters may be able to change it from one definite outcome
to another.

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