At 10:40 AM 2/2/2010, Kristofer Munsterhjelm wrote:
With truncation and more than two candidates, obviously the number
of piles are greater (because the set of fully-specified candidate
orderings, of which there are C!, is a subset of this). With
truncation and equalities, greater still.
Except for the Australian anomaly, where they imagine that a
"majority" with some percentage of coerced votes is a real majority,
or some versions of Borda which penalize, to a lesser degree, voters
who don't fully rank, all voting systems allow equal ranking, but
many or most only allow equal ranking at the bottom!
I can see no rationale for this asymmetry, beyond a continuation of
the vote-for-your-favorite habit that actually made sense within the
context of repeated balloting until a majority was found. As I've
pointed out, repeated ballot, no eliminations, majority required, is
an extremely powerful voting system; for starters, it's Condorcet
compliant, but the repeated balloting allows for adjustments, i.e.,
voters can change their mind once they understand how other voters
feel, so it *also* is more social utility maximizing than a pure
single-ballot Condorcet method would be.
Be that as it may, vote-for-one has an appeal and a power, for it
allows voters with only enough information to know who their favorite
is to vote intelligently. Asset takes full advantage of this. But
voters, more generally, can classify candidates into four categories:
Prefer
Acceptable
Unknown
Disliked.
A voting system that collects more accurate category information is
likely to perform better. Forcing voters to over-categorize (the
extreme is full ranking, even if approval cutoff is specified)
generates noise, but it may not be random noise, under-categorization
eliminates real voter preferences.
There is a difference between Unknown and Disliked which the method
might interpret usefully. There is a difference, as well, between
preferred and acceptable, and I see utterly no reason to prevent
voters from equally categorizing candidates. We should have had
approval voting long ago, and the reasonable comparison should be
between approval voting and vote-for-one, not approval vs.
preferential balloting, approval is simply a more efficient form of
"plurality," with the same two categories, preferred and rejected,
only with the voter now able to freely categorize using the two.
I do expect this argument to eventually prevail, so that the *worst*
voting system comes to be Approval Voting. Repeated ballot, though,
is so flexible that in many elections, approval would be fully good
enough. But beyond that, I'd want to collect preference strength
information through a range ballot with explicit approval cutoff.
Repeated ballot has many safeguards built in; for starters, anyone
who voted with the majority can generally move to reconsider the
question (when it's not secret ballot), and similar rules could be
developed for use with secret ballot, a reconsideration is voted on
immediately, no debate. That is, to reconsider or not is voted on. If
the reconsideration passes with a majority, the original result is
essentially void, the question is reopened.
Approval in many elections reduces *almost* to Plurality. This has
been cited as an argument against Approval. In fact, it's an argument
for it. The same is true for Range, which reduces to Approval if
voters bullet-vote, which many expect (falsely, probably). Bucklin, the same.
In fact, even *more*, IRV, the same. We are not seeing any results in
*nonpartisan elections* where IRV results are any different from what
we would see if voters simply voted for their favorite!
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