[EM] Re: The Allure of IRV

[Richard Moore]

Dave Ketchum wrote:
>> Preferences that are expressed in Approval tend to be strongly held
>> preferences, while preferences that are expressed in ranked ballots
>> are of unknown strength (and sometime negative strength, particularly
>> in non-Condorcet methods such as IRV and Borda). Thus, the voters may
>> end up with a CW who is favored by a majority of voters to all other
>> candidates, but who doesn't have any voters that have a strong
>> preference for that candidate over their next choice. When the CW and
>> the AW (Approval Winner) are different, the better choice is probably
>> the AW, since it is likely that, for the majority that prefer the CW
>> to the AW (as indicated on rank ballots), that preference is a weak
>> one -- otherwise that preference would be expressed in the Approval
>> vote as well. For the minority who approved the AW without approving
>> the CW, this was more likely to be a strong preference.
> 
> 
> 
> I get dizzy, and suspicious, trying to sort that out.

Hmm, I might suggest a little more effort, rather than simply dismissing
an argument because it makes you "suspicious". Still, I guess more clarity
wouldn't hurt (I wasn't intentionally trying to be confusing, but I can
see that my words came out less clear than I intended).

So, let's say you have an election in which two sets of ballots are taken
simultaneously: one ranked set, and one approval set. The ranked ballots
are counted to find the CW, and the approval ballots are counted to find
the AW. If CW and AW are the same, then neither method has bested the
other. If CW and AW are different, then...

1) there is a majority N1 of voters who prefer CW to AW. Some of these
will have approved of CW and disapproved of AW; call this number N1A.

2) there is a minority N2 of voters who prefer AW to CW. Call the number
of voters within this group that approved of AW and disapproved of CW
N2A.

For simplicity I'll assume nobody voted any tied preferences between
AW and CW.

Since AW is the approval winner, we know that N2A > N1A. We also know
that N1 > N2, meaning that (N2A/N2) > (N1A/N1). That is, the voters
who prefer CW to AW are less likely to express that preference on an
approval ballot, than the voters who prefer AW to CW are to express
that preference on an approval ballot. In other words, we have a good
reason to believe that the median strength of the CW>AW preferences
is less than the median strength of the AW>CW preferences.

I don't claim that the Approval winner is always more strongly preferred
than the Condorcet winner when the two differ, but I think I've shown
that such will be the case more often than not. Hence, I am more willing
to trust Approval than Condorcet.

(On the other hand, I can't think of a single argument to justify the
IRV winner over the Condorcet winner, when those two methods give
different results.)

> Truly the decision as to winner is a public choice, but it needs to be, 
> as close as possible, the sum of the private choices of the voters.  For 
> that to work, knowing more of what each voter's private choice is needs 
> doing so far as practical.

"...as far as practical" -- indicating that there are practical limits
to allowing individual expression. I think Approval does at least as
well as Condorcet at aggregating individual choices. If I have a weak
preference for A>B, and a strong preference for B>C, then voting a
ranked ballot of A>B>C adds more noise than voting an Approval ballot
of AB.

>> If it's individual expressivity you want, then Cardinal Ratings are
>> for you. You'd be perfectly free to sacrifice instrumental voting power
>> to make a more exact statement about your evaluation of the candidates'
>> merits.
> 
> 
> 
> This one scares me.  I would worry about losing to those who could figure
> out a strategy to give themselves extra power over those of us who are
> not up to strategy.

I suggested CR as a counter-example to the notion that maximizing individual
expressive power should be an end goal of choosing an election method.

Actually my worry about CR is the corollary to yours. While I would simply
vote an Approval-style ballot in CR, if other voters who are on my side
aren't up on this strategy, and vote their actual ratings, then I could
lose. Approval is a way of doing CR that levels the playing field between
the strategy-aware and non-strategy-aware voters.

>> If you are unable to decide whether to approve or disapprove some
>> candidate, because that candidate is somewhere close to the strategic
>> borderline between approval and disapproval, then the strategic value
>> of your vote for that candidate is close to zero (relative to your
>> strategic values for the high- and low-utility candidates). Therefore
>> the strategic cost of making the wrong choice on this particular
>> candidate is very low.
> 
> 
> 
> I think you are saying it is not important whether I get it exactly 
> right - could be, but I am not sure where the ballpark is, to be close 
> to being right.

That's pretty much what I was saying. A wrong choice made near the
utility extremes could negate the power of your ballot altogether, but
you aren't likely to make a wrong choice there. Near the middle of your
utility range is where you are most likely to make a wrong choice, but
the damage to the value of your ballot is going to be very minimal in
such a case.

> Adam was more helpful, with a rule I could follow:  Approve whichever 
> candidate I prefer among the expected front runners, and approve all the 
> candidates I like better than that one.

I thought the various simplified approval strategies had already gotten
a lot of exposure on this list in recent weeks, so I didn't want to be
too repetitive.

  -- Richard

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