[EM] Real IRV Election, Disputable Result

[Jan Kok]

On 3/12/06, Jonathan Lundell <jlundell at pobox.com> wrote:
> At 1:57 AM -0700 3/11/06, Jan Kok wrote:
> >I crunched the election data and found that Kiss was preferred to
> >Miller, 4755 to 3988.
> >
> >Drat. :-)
>
> That's still not numerically consistent with the published Burlington
> results; I wonder what the discrepancy is.

I think it might have to do, at least in part, with how equal-rankings
are counted.  Equal-rankings were allowed and reported in the
Burlington data.  (The way it was handled for IRV seemed a bit
inelegant, though.  It seems that if you rank two or more candidates
in _first_ place, your ballot is "exhausted", which I guess means it
doesn't count.)  When I counted Kiss vs. Miller 4755 to 3988, I didn't
count any of the Kiss=Miller votes.  I just now checked one of my
intermediate data files and saw that there were 13 ballots that ranked
Kiss=Miller(=others sometimes).  If you want to give each 1/2 point
for the equal ranking, then the score would be 4761.5 vs. 3994.5
(according to my count).

> Let me dispute your "drat", though. Your thrust, I suppose, is that
> you'd like to find an IRV election in which there was a Condorcet
> winner not elected by IRV.

Yes.

> I suggest that this quest is based on a
> fallacy, and that such a result could not legitimately be used to
> argue the merits of IRV vs Condorcet ranking.

Well, there are a lot of IRV supporters who are political activists,
but don't have very good math and logical reasoning skills.  (I
_don't_ include you in that class, Jonathan.  You are obviously light
years ahead of the average IRV advocate.)  Many of them are only
familiar with the rosy descriptions of IRV promoted by CVD, and so
they have no idea that IRV can fail to elect the Condorcet winner
(many don't even know what that means), or that there can be
situations where there is an incentive for some voters to vote
strategically, or that adopting IRV can be substantially more
expensive (in equipment upgrades and education of voters and election
personnel) than other methods, or that IRV data can't be succinctly
summarized at the precinct level, thus making it harder to insure
election integrity.

I have corresponded with one IRV supporter who (apparently)
understands that IRV and Condorcet elections are counted differently,
and would probably grudgingly admit that they can choose different
winners with made-up example sets of ballots, but adamantly refuses to
believe that IRV and Condorcet can get different results in a
"real-life" election.  And there are other IRV supporters (including
myself in the past) who are vaguely aware of alleged problems with
IRV, but don't believe the problems are serious, because they don't
believe the problems will occur very often ("Can you show me an
example of a real-life public election where that problem occurred?"),
or they don't understand the real-life implications of these
technical-sounding problems.

An example of Condorcet failure in an IRV election might help wake up
some of those IRV supporters.

> I'm not arguing the merits of IRV vs Condorcet here; I go back and
> forth on the question myself. I'm only arguing against the validity
> of a particular sort of evidence.
>
> The fallacy lies in different voter behavior.

I think I understand your point.  You're saying that voters would vote
differently depending on whether the election was to be counted with
IRV or Condorcet.  Therefore, it's not valid to take a set of ballots
that were intended to be counted with IRV and count them with
Condorcet.

My reply:  Under IRV, there are situations where there is an incentive
for some voters to vote insincerely.  For example, suppose the sincere
preferences are:

41 A>B
10 B>A
10 B>C
39 C>B

If all voters vote their sincere preferences, A wins.  This is the
worst outcome, from the viewpoint of the C>B voters.  The C>B voters
can obtain a better outcome by voting B>C instead.  If at least 10 of
the C>B faction change their vote to B>C, then B wins.  So, in this
case, there is an incentive for the C>B voters to vote strategically. 
Note that the effect of the strategic voting is to cause the Condorcet
winner (according to sincere preferences) to get elected.

Given the same set of sincere preferences as above, there is no
incentive for any voters to vote insincerely in a Condorcet election. 
(The A>B faction could truncate and just vote A, but B would still
win.)  I believe that, in general, there is no incentive for any
voters to vote insincerely in a Condorcet election, provided that
there is a Condorcet winner in the sincere preferences.

If there is no CW in the sincere preferences, then there will be
incentives to vote strategically in IRV _and_ Condorcet.  In that
case, the situation becomes very difficult to analyze, and I would
rather ignore that possibility and hope it doesn't happen :-).  (If
pre-election polls as well as actual ballots consistently showed a
Condorcet winner, and the candidates fit into a left-to right spectrum
ideologically, that would be evidence that there was indeed a CW in
the sincere preferences, and that there would be no incentive for
voters to vote strategically if the election was counted with
Condorcet.)

At any rate, I think the incentives for strategic voting occur much
more often with IRV than with Condorcet.  If Condorcet gets a
different winner than IRV when applied to ballots from an IRV
election, I think the burden of proof would fall on the IRV advocate
to show that the CW determined from the ballots was not the true CW,
or that there was no CW.

I expect that if/when we find an IRV election that fails to choose the
CW, it will be a center-squeeze situation such as my example above.

> IRV and Condorcet
> ranking come with different guarantees to the voter. An example (and
> there are examples on both sides) is that IRV guarantees
> later-no-harm. That is, the IRV voter can freely rank lower choices
> with the assurance that those choices cannot harm the chances of the
> voter's earlier preferences.
>
> Condorcet ranking does not (and cannot) make that guarantee. So the
> same set of voters (in Burlington VT, say) faced with the same
> candidates but a Condorcet rather than an IRV election, are likely to
> cast different ballots. So to take an election profile that was made
> under IRV rules and apply Condorcet ranking to it might be of casual
> interest, but it's an apples and oranges comparison.
>
> I'm not claiming that later-no-harm is a decisive argument in favor
> of IRV; Condorcet ranking has its own advantages, and later-no-harm
> is not IRV's only advantage. I'm only arguing that you mustn't change
> the counting rules after the election without also giving the voters
> a chance to change their ballots in view of the alternate rules.

I think it's highly unlikely that a public election would ever be held
asking voters to vote with two ballots, one to be counted with IRV and
one to be counted with Condorcet (with a coin toss, for example, to
choose the winner if the two methods give different results.)  So, the
best we can do is use the ballots of real elections, hope that voters
voted either sincerely or in a rational, strategic fashion, and try to
compensate, based on our understanding of voter incentives, as well as
other information about the candidates and the campaign, to determine
what voters' sincere preferences were.

> All this is further complicated, of course, by the fact that voters
> are human, and are neither perfectly informed nor perfectly rational.
> But they're somewhat informed, and somewhat rational, and we must
> expect that the specific election rules in place will have some
> effect on voter behavior.

Yes, I agree that the election rules affect how people vote.  But,
unsophisticated IRV supporters are not aware that there can be
incentives to vote insincerely in IRV elections, or may believe that
IRV and Condorcet will always, or almost always, choose the same
winner.  If we can find a counterexample (even if somewhat flawed
because the ballots were intended to be counted by IRV and not
Condorcet), it may wake up some IRV supporters and get them to at
least question, "If these two methods can get different results, which
method gives the better result?"

> --
> /Jonathan Lundell.

Cheers,
- Jan