[EM] Saari & Borda contd.

[MIKE OSSIPOFF]

EM list--

I've just realized that I missed Saari's correction at the
beginning of his letter. His remark about  electing a Condorcet
losser referred only to non-pairwise methods that meet the
Majority Favorite Criterion, I realized when I noticed the
correction.

I don't have the copy of his letter right here, but he says
that pairwise-count methods have other serious difficulties
that he doesn't specify there. Difficulties like his example
that was posted here, where the addition of some voters
changed the outcome, even though those new voters, by themselves,
would have made a symmetrical circular tie?

He says that it isn't about separate ballotings before & after
the voters are combined, but that it's about looking at
different parts of the set of ballots from one balloting.
If that weren't so, I'd object that voters strategize differently
when they're in a different electorate.

But I don't understand why it's important what those 2 separate
subsets of the ballots would do if they were separately counted--
they aren't separately counted, so what meaning does the idea
have? Who's wronged? Who'd protest the outcome or be forced
to strategize to avoid it?

***

It seems to me that if one could object to that example, it
would be by saying it in terms of a criterion like this:

If a subset of an elections ballots, counted separate from the
rest, would result in a tie, then the count result shouldn't
be changed if those ballots aren't counted.

***

If I refer to that again I'll call the it Independence from Tied
Voters Criterion (ITVC).

The Consistency Criterion doesn't seem important for the same
reason as ITVC. If it were construed to about separate ballotings
before & after voter subsets are combined, then I could say
that people wouldn't necessarily vote the same in both situations.
If it's merely about looking at different subsets of the ballots
from one balloting, then I don't understand the importance of
that.

But hasn't Saari mentioned Consistency as an advantage of
Borda? Approval meets ITVC & Consistency, and it beats
Borda at its own game by meeting a Consistency-related criterion
that's about candidates instead of voters:

Deleting from the ballots one or more losing candidates shouldn't
change the matter of who wins the count. (No new balloting is
conducted; the same ballots are used, with the deletion(s) ).

(It seems to stand to reason that if you delete from a Plurality
ballot the candidate that someone voted for, then it becomes as
if that voter had turned in a blank ballot. Deleting from an
Approval ballot a candidate for whom that voter voted removes
his name and the vote for him. Deleting a candidate who is voted
for in a ranked ballot means that the other candidates in the
ballot are renumbered according to their rank position when
the deleted candidate isn't there. That's all agreeable isn't it?)

***

That sounds similar to IIAC, and it makes me realize that I
don't know really know what IIAC is.

Anyway, Approval meets that criterion, and Borda fails it.
I wonder what can be said for Borda but not for Approval. Maybe
I'll find out from Saari's new letter, arrived today on the
list, which I haven't read yet. And maybe that letter will tell
what serious difficulties all pairwise methods have that
Borda doesn't have. If it's only ITVC, or the example I
discussed in this letter, then I don't count that as a difficulty,
much less a serious one.

I should check that new letter out, but any advantage or
criticism of a method seems a little questionable when it can't
be stated in a brief paragraph.

Mike Ossipoff





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