LO2E-2 Criterion

[Blake Cretney]

On Sun, 4 Oct 1998 00:32:04    Mike Ositoff wrote:
>
>LO2E-2:
>
>If a majority of all the voters vote some particular alternative
>A over some particular alternative B, then they should have
>a way to ensure the defeat of B without anyone having to vote
>A equal to or over an alternative that he/she likes more.
>
>***
>
>It's quite obvious that there's no way that Margins could meet
>that, since it loses information about majorities when it
>subtracts.
>

If a majority of voters rank B last on their ballots, then it will have
a pair-wise loss against every other candidate.  So any method that
passes the Condorcet Loser criterion will pass LO2E-2.  This includes
Schulze (Margins and VA) and IRO, but excludes Simple Condorcet (Margins
and VA)

Here is an example for Votes-Against, which shows that Votes-Against
Simple Condorcet violates what I think you intend as LO2E-2.  Perhaps
more importantly, it does so because the D voters have simply filled
their ballots randomly instead of leaving candidates unranked.  I have entered an  equal number of D voters as voting for each permutation of
A, B, C.  Of course, you wouldn't get such an even distribution for only
18 votes, but this example can be extrapolated out to larger numbers.

7 A B C D
7 B C A D
7 C A B D
3 D A B C 
3 D A C B
3 D B A C
3 D B C A
3 D C A B
3 D C B A

   A   B   C   D
A  X   23  16  21
B  16  X   23  21
C  23  16  X   21
D  18  18  18  X

The winner with both marginal and votes-against Simple Condorcet is D.
Now, a majority of 21 to 18 prefer either of A, B, or C to D.  I suspect
that any way they change their votes would be called accepting the lesser
of two evils.

>Approval guarantees that when a majority votes A over B,
>B can't win, and preventing B from winning doesn't require
>anyone to vote a less-liked alternative over a more-liked
>one. Margins fails to be as good as Approval in that regard.

Is this the version of Approval that can trigger a new election.  If
so, is there any way a majority of voters can prevent that outcome
without accepting a lesser of two evils?

***

>If a majority of all the voters vote some particular alternative
>A over some particular alternative B, then they should have
>a way to ensure the defeat of B without anyone having to vote
>A equal to or over an alternative that he/she likes more.

I would also like to suggest a possible redraft of LO2E-2.  It is 
unclear whether lowering A is an allowed strategy, I am assuming you
don't want this.  Also, it is possible there could be multiple 
candidates the majority would want to prevent.

Suggested LO2E-2 redraft
Consider a set of alternatives (P), where some alternatives are not
in P. If a majority of ballots rank all members of P bellow all 
alternatives not in P, then the winner must not be in P.

Blake



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