[EM] approval vs. IRV: majority loser criterion

[James Green-Armytage]

Adam Tarr writes:
>You've shown that approval is exactly as bad as plurality, when people 
>choose to vote in exactly the same way as plurality.  This should come as 
>no surprise to anyone.  If everyone bullet votes in IRV or Condorcet, it 
>would have this same effect as well.
>
>One would imagine that the voters in your example would be aware of the 
>fractured nature of their faction, and willing to cast a vote for the 
>universal second choice.  Your electorate is behaving in an amazingly 
>irrational way.

	Adam, I know, I know. Of course you're right. The first example I gave
was nuts, and I admitted it as soon as I got done writing it. That's why I
wrote the second example:

sincere preferences, plus approval cutoffs:
20: A>B>>L
10: A>>B>L
15: B>A>>L
7: B>>A>L
48: L>>A>B

	L, the majority loser, wins this approval election.
	This is not necessarily an amazingly irrational electorate. It is simply
an electorate that was unable to resolve the tricky cooperation/defection
example which is present in approval voting. Probably you have heard that
argument before, but let me quote from my survey:

<beginning of quote>
45%: Conservative
30%: Labor > Democrat > Conservative
25%: Democrat > Labor > Conservative
           Approval voting in itself offers no mechanism to resolve this
kind of situation. If the Labor and Democratic voters unite in approving a
candidate, then that candidate will beat the Conservative, something that
both Labor and Democratic voters want. But which will be the winner, Labor
or the Democrats? 
            If all of the Labor and Democratic voters approve both the
Labor and Democratic candidates, then there will be a tie. If all of them
except one approves both, and the remaining one only approves the
Democrat, then the Democrat will win. If one voter only approves the
Democrat, and two only approve Labor, then Labor will win. Thus both
Democratic and Labor voters have an incentive to approve only one, but as
the numbers grow who follow this incentive, the chances of electing the
Conservative increase. 
            The result is essentially a game of chicken between the Labor
and Democratic voters, where approving both candidates is analogous to
swerving, approving only their favorite candidate is equivalent to staying
on course, and the car crash is the election of the Conservative. Needless
to say, this is a messy and chaotic way to elect a president. 
<end of quote>

	This sort of situation is one of the major trouble spots for approval
voting. It is an issue that we have already discussed, and there are
arguments on both sides as to how severe a problem it is, but I'm just
using it here to argue that the second example is neither implausible nor
irrational. There is a strong motivation for A and B voters to cooperate,
but there is also a strong motivation to defect. Hence it is possible that
mutual defection could throw the election to the majority loser
	I haven't made a statement yet about how likely it is that approval will
select a majority loser. All I have demonstrated is that it is possible,
and that approval fails the majority loser criterion as I have defined it.

best,
James