[EM] Use a turkey filter
Bart Ingles
bartman at netgate.net
Sun Jul 6 15:02:10 PDT 2003
Anthony Duff wrote:
>
> I think the turkey issue is a real problem for
> condorcet and approval. A simple solution is to
> filter out the turkeys before they get on the ballot.
I think this would have the opposite effect, in that it stifles real
competition. Although ballot access restrictions are somewhat
understandable when the method in use is Plurality.
> Consider the Australian example. Ballots are ranked.
> Equal rankings are not allowed, except that truncation
> sometimes is. The count is conducted by IRV, not
> Condorcet, but I argue that that is nearly irrelevant
> – the masses are fully occupied , 1st, with decided
> which candidate they will prefer, and 2nd, with
> following the instructions on how to complete their
> ballots. Few enough understand the mechanics of vote
> counting, let alone analyse it.
>
> A typical result is (seen often enough during the
> physical sorting of ballots):
>
> 45% left>centrist>right
> 5% centrist>left?right
> 45% right>centrist<left
> various other candidates randomly interspersed.
>
> The centrist candidate is arguably a turkey who is
> eliminated by IRV but who would win under Condorcet.
>
> The important factor that leads to the above voting
> pattern is not a rational strategy, but the
> psychological urge to put your favourite’s most
> serious opponent *LAST*. After all, the elector's
> favourite will have been most lengthily denouncing
> that main opponent. Some other candidate will find
> themselves last an anyone’s ballot only if they are
> seriously repugnant.
I think it's necessary to distinguish between worst-case scenarios, and
typical behavior (i.e. "a tendency to elect bland candidates").
When I first joined this list, I supported IRV over Condorcet (I hadn't
yet learned about approval voting) because of the Condorcet worst-case
scenario approximated above. More specifically, if we show not only
rankings, but voter ratings on some scale, say 0-100, a near worst
three-candidate Condorcet example is:
Example 1:
49% left(100) > center(1) > right(0)
2% center(100) > left(0) = right(0)
49% right(100) > center(1) > left(0)
The ratings are necessary to distinguish from the near best-case
Condorcet scenario:
Example 2:
49% left(100) > center(99) > right(0)
2% center(100) > left(0) = right(0)
49% right(100) > center(99) > left(0)
Of course I'm making some obvious assumptions, such as that the factions
are monolithic, that all voter ratings are normalized on a scale of
0-100, and that there are no viable candidates other than the ones
listed in the examples, etc. I'm trying to make this intuitive and
illustrative, rather than scientific.
Note that the above is worst-case in terms of choosing a winner with
very low average ratings (approaching zero). There are other kinds of
worst-cases, such as looking for the largest possible ratings deficiency
between the highest rating-getter and the actual winner. In example 1,
the Condorcet Winner (CW) has an average rating of about 3, while the
top rated candidates average 49 each. So the winner's rating deficit in
this example is 46. Note that with Condorcet, the worst-case rating
approaches zero, and the worst case ratings deficit approaches 50,
regardless of the number of candidates.
For an IRV worst 3-candidate example:
Example 3:
49% left(100) > center(99) > right(0)
25% center(100) > right(1) > left(0)
26% right(100) > center(99) > left(0)
Here Center loses with a near-perfect 99+ rating. Right wins with an
average rating of 26 and a rating deficit of 73. In the three-candidate
case the mininum winning rating approaches 25 (somewhat better than
Condorcet), and the maximum deficit approaches 75 (somewhat worse than
Condorcet. As the number of candidates increases, the minimum winning
rating declines exponentially, so with more than 4 or so candidates it's
not appreciably better than Condorcet, and the maximum deficit
approaches 100, or about double that of Condorcet.
The worst 3-candidate Approval example I can find (for a zero-info
election):
Example 4:
49% left_a(100) > left_b(51) > right(0)
2% left_b(100) > left_a(49) > right(0)
49% right(100) > left_a(49) > left_b(0)
Here the voters are following the better-than average strategy,
approving of all candidate that they rate better than 50. Here left_b
wins with 51% of the vote and an average rating of 27, while the highest
rated loser (left_a) has an average rating of 74 (for a deficit of 47).
The minimum winning rating for three candidates approaches 25, similar
to IRV, and the maximum deficit approaches 50, similar to Condorcet. As
far as I can tell, as the number of candidates increases the minimum
rating for a winner declines geometrically-- not quite as fast as with
IRV, but still approaching Condorcet's zero. But the maximum losing
rating also declines, so that the max deficit hovers just over 50 (much
better than IRV, and nearly as good as Condorcet).
Conclusion #1: when considering both the minimum winning utility, and
the maximum utility deficit of the winner, IRV is inferior to the other
two methods with three candidates, and it grows worse with additional
candidates.
When looking at typical cases or tendencies, we don't have the empirical
data on either Condorcet or Approval in highly political elections to
prove whether or not the candidates will be bland. But in my view the
existing Plurality/IRV situation results in "chocolate vs. vanilla" even
if the two do appear to be campaigning vigorously against one another.
This is fine if you happen to like chocolate or vanilla, or if you think
the chocolate-vs-vanilla debate is the most important question to be
answered. If not, if you think both parties are avoiding the important
issues, you are likely to view the existing choices as being the real
turkeys.
Bart
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