How to vote in Approval

[MIKE OSSIPOFF]

The question was asked:

Forest mentioned my favorite Approval strategy: Approve every candidate you
prefer to the current frontrunner; approve the current frontrunner if you
prefer him to the current second-placer. What are some other good 
strategies?

I reply:

Two authors, who might have been Tideman & Merrill (but I'm not
sure) suggested some Approval strategies similar to that one.

In an article that Approval advocate Jon Schulze sent to me around
1990, the authors suggested holding 2 Approval ballotings, the 1st
one just a straw-poll to provide information for the 2nd balloting.

They discussed several strategies, based on the information in the
1st balloting.

One of them was: Vote for everyone better than the mean utility of
the 2 frontrunners. But why vote for someone whom you like less than
the more preferred of the 2 frontrunners? Why vote any lower than you
need to? An answer to that is that if we don't know which of the
2 frontrunners is more likely to win, and if there's someone whom
you like better than the lottery between those 2 frontrunners, then
why not vote for that candidate.

Maybe a more general rule would be to just say to vote for everyone
whom you like better than the lottery between the 2 frontrunners,
given the utilities for you, and the win-probabilities of the 2
frontrunners.

So both strategies sound plausible--voting down to the more preferred
of the 2 frontrunners, and voting down to the candidate who's barely
better than the value of the lottery between the 2 frontrunners.

Of course estimating who the frontrunners are going to be sounds a
lot easier than trying to estimate everyone's win-probability, as
I did when I determined how to vote in the SF mayor election. I like
the frontrunner approach better, because it seems more reliable
guessing who the frontrunners will be than guessing everyone's
probability of winning.

As for the 2 Approval ballotings, that would be a good thing, of
course, but I don't know if it would be a winnable proposal. Adding
that extra balloting to nonmunicipal elections would be resisted.
And my conversation with a progressive Berkely councilmember suggests
that keeping more than just the top 2 votegetters in the 2nd balloting
would also meet with great resistance.

Maybe the choice is between pure 1-balloting Approval, and
Approval with top-2 runoff. I prefer the former, but maybe the
latter would be easier to get. Still, it seems better to first try
for what's better, before resorting to something that doesn't seem
as good.

Cranor's (Crannor's ?) web article about Pivotal Probabilities
(if I correctly remember the name of the webpage) talks of ways
of estimating the Pij. Hoffman's method sounds good, except that
when the number of candidates exceeds 4, the computational work
increases and the number of dimensions exceeds 3. More dimensions are
added as more candidates are added.

Cranor suggested a method that avoids the problem of Hoffman's method,
but, for me at least, there didn't seem to be enough information to
make her method clear. If anyone understands Cranor's method, would
they explain it here?

By the way, I've heard that Plurality DSV doesn't necessarily converge,
when there's a cycle. Does Approval DSV converge reliably anyway?

Oh, one other thing: I'd said that I consider the Democrats & Republicans
unacceptable, and wouldn't vote for either in Approval. Though that's
how I'd have voted if Approval were used in 2000, I now have to admit
that it isn't how I'd have voted in Approval in 2000 knowing what
I know now. More information about the would-be Bush administration
would have forced me to not say that the ordinary Democrats & Republicans 
are completely unacceptable. I'd have divided the candidates
into 3 merit levels: Nader (and maybe other progressives); ordinary
Democrats & Republicans; and Bush. And I have to admit that I _would_
have voted for Gore in Approval in 2000 if I knew what I know now
about the candidates. If other Democrats & Republians were in the
election too (if it were a no-primary single-balloting election), then
I'd have voted for them too.

If Condorcet(wv) were used, though, I probably wouldn't have used
Approval strategy in Condorcet, wouldn't have voted everyone but
Bush in 1st place. I'd have voted the 3 merit levels that I named
above. Nader in 1st place; ordinary Republicans & Democrats in 2nd
place. By so doing, I'd be giving up a possible chance of stopping
Bush from winning in some special natural circular tie, but if there
were a majority against Bush, as described in the majority defensive
strategy criteria, Bush would lose without anyone using Approval
strategy. I'd probably have trusted that the other voters would
make that majority, so that that ambiguous situation where Approval
strategy would help wouldn't happen.

Mike Ossipoff




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ALL methods have problems with 3 or more choices due to having divided 
majorities (if there is no first choice majority).

2 examples -- Initial votes in each example

26 AB
25 BA
49 Z
100

--------
34 ABC
33 BCA
32 CAB
99

Who, if anybody, has a YES majority ???

If the initial polls do show any such YES majority, then do some folks start 
playing strategy games ???

Standard comment--- The election ends when the polls close and the votes are 
counted according to the method being used.

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Adam wrote in part-

One final thought.  on 3/20 I posted a message about Approval Completed 
Condorcet.  The idea was to use a graded ballot (ABCDEF, for example).  If 
there was not a Condorcet winner, then the candidate with the most approval 
votes (A's, B's, and C's in the case of ABCDEF ballots) wins the 
election.  In my initial analysis, this method seemed at least as good as 
the other Condorcet methods we like to discuss.  Furthermore, it seems like 
it could be an easier method to pitch, since the cycle-breaker is VERY 
intuitive.  So I guess what I'm asking is... does ACC render this whole 
debate meaningless?  Just a thought.
---
D- I noted ACMA long ago -

Approval
Concorcet
Most Approved tiebreaker (if no Condorcet winner).

Approval by itself is defective since it does not rank the Approved choices.

Condorcet by itself is defective since it does not indicate that a choice is 
approved.