[EM] Majority-Choice Approval

[Forest Simmons]

On Tue, 7 May 2002, Joe Weinstein wrote:

> Majority-Choice Approval does have a slight drawback: ‘inconsistency’.  In
> its procedure for deciding a winner, the method is a hybrid: it works one
> way under one condition and another way under another condition.  As for
> almost all such hybrids, the method is inconsistent, in the sense that a
> candidate A may win all precincts but not the entire electorate.

Good insight about hybrids!

> Here this inconsistency can occur if A wins some precincts on account of
> being majority favorite; but wins other precincts, which lack majority
> favorites, on account of being most approved.
>
> For instance, consider an electorate of two five-voter precincts, and a
> contest among five candidates A-E.  Each marked ballot favors exactly one
> candidate X and accepts exactly one other candidate Y - symbolized below by
> the format XY.
>
> Ballots in precinct #1 are:    AB, AB, AB, CB, DB.
> Ballots in precinct #2 are:    AB, BA, BA, CA, DE.
>
> A wins precinct #1 as the majority choice and precinct #2 as the most
> approved; but B wins the entire electorate as the most approved.
>
> For Majority-Choice Approval (unlike some other methods) such inconsistency
> is easy to accept.  The reason is simple: we prefer a majority favorite,
> which we may in fact happen to get in some precincts but do not necessarily
> expect to get overall.

Nice example and nice apologetics :-)

I have argued before that Condorcet's consistency failure is easy to
understand and accept because it happens only when there is no CW in all
of the subsets (i.e. precincts), so that some of the precinct winners are
not as decisive as others.

On the other hand, IRV fails consistency in cases where all of the subset
victories are by decisive (IRV style) majorities, i.e. the kind of
majorities that IRVists claim as decisive.

Forest

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