At 09:13 PM 5/20/2010, [email protected] wrote:
Thanks for the comments Kevin and Lomax.
Let me start over in the same vein:
Suppose that candidate X was just announced as the winning candidate, and no
indication was given of how the other candidates fared in the range
style election.
How would you wish that you had voted your range ballot?
Weird circumstance, eh? I don't know how close it was?
Personally, I would be mostly satisfied with my ballot if I had given max
support to everybody that I preferred over X, and no support for
anybody I liked
less than X.
Sure, the same. But that's not the only ballot I'd feel satisfied
with. In particular, if I had a favorite, not just some candidate who
I thought was totally irrelevant, and I rated someone else the same
as that candidate, I'd not be happy. Because I didn't express my
preference, even though it was, in the end, irrelevant. If it's going
to be that the other results are never announced -- what kind of
system is this? -- then that expression is completely moot. It's not
moot in real elections, unless there is massive fraud.
But what about X ? I could say that since X was the winner, X probably didn't
need my support, so I would wish that I had not supported X at all. But if
everybody took this attitude, then everybody would regret their support for X,
except those that preferred X over all of the other candidates. And
most likely
X could not have won with support only from those who considered X
as favorite.
That is contrary to your initial condition, probably.
Suppose that due to some technicality the election had to be repeated. Would
you give any support to X this time around (still not knowing
anything about how
the other candidates fared) ?
Well, I'm proposing Range ballots feeding Bucklin "instant runoff
approval." So I'd know from this far more about the preferences of
others, and I could make my choices over a real understanding of
probabilities. I'd already know if and what other candidates had some chance.
But, given the highly artificial constriction, I know nothing more
than I knew in the first place. Forest, you set the condition that X
was very likely to win. That's all you know for the second ballot,
why should your decision be different?
In my last message under this topic I suggested that perhaps the
thing to do in
the case of a sure or almost sure winner (when you know nothing about the
chances of the other candidates) is to just give them your sincere rating.
Yeah, that part is correct, I believe. However, if you know the
identity of the frontrunners, you can make a better choice. But not
much better!
The only place where there is a problem with "sincere voting" is when
the "sincere ratings" are distorted by the presence of irrelevant
candidates about whom you have strong feelings (for or against).
Sincere ratings can be constructed by asking questions like this: Would I
prefer X to a lottery of 31%favorite+69%worst? Suppose that the
answer is yes,
but when the same question is put with the percentages changed to 29
and 71, my
answer changes to no. Then my natural rating for X would be about 30 percent.
What is the point of all of this? I'm looking for a DSV (Declared Strategy
Voting) method that takes sincere natural ratings and converts them into
strategic range ballots in such a way that when the winner is announced, the
voters will be as satisfied as possible with the way the DSV handled
their ballots.
Bucklin. It's been done, to a degree. The ballot becomes clearer in
meaning if the election requires majority approval; this ties
approval to voter preference for a resolution in the first ballot vs
the risk and inconvenience of a runoff. So "approval" means "I
approve this candidate in preference to holding a runoff election
under the rules."
If most voters prefer to see a runoff, it certainly seems fair to me
to hold one!
For practical voting methods, for public use, I believe that it is
necessary that the method of using the votes be very clear and
simple. I'd allow a little more complexity, but not much more, in
determining who is in a runoff election if one is to be held.
Eventually, with a lot of ballot experience, it might be possible to
eliminate more of the runoffs, but it would start, I'd suggest, with
a runoff whenever no majority is found. Because some elections with
majority failure make it obvious who would have won, among the
possible choices, in an "instant runoff," because the margin is so
close and nobody else is in range of winning, it does seem prudent to
allow some elections to complete short of a majority. With good
ballot data, it's possible to measure the regret involved and to make
this decision in a far more accurate way than simply requiring a
fixed percentage. The use of 40% in Burlington is *awful*....
Bucklin was used, was very popular, is easy to count, and makes the
most sense as a primary method in a runoff environment, seeking a
majority. It was never used for that; like IRV, it was sold as a
runoff replacement. Bad Idea. Sometimes the electorate doesn't have
enough information to make up its mind!
Bucklin is like a declared strategy method, if I understand the idea,
where one has a bot voting for you in a series of approval elections,
where the bot adds in additional approvals according to the "round
number," using your ratings of the candidates to decide when to vote
for you for any given candidate, if ever. The ranks on an original
Bucklin ballot are the approved ratings from a Range 4 ballot, and
they had the original restriction that overvoting in the top two
ranks was prohibited, I'd dump that, there is simply no justification
for it. (Bucklin gives so much freedom to express the Favorite that
it's silly to worry about multiple majorities in the first rank and
therefore possible Majority criterion failure. In reality, majority
failure seems to be, long-term more likely, though Bucklin was, in
municipal elections of high interest, very good at finding
majorities. Only people who have no significant preference will vote
for more than one candidate in first rank.)
Original Bucklin allowed skipping ranks, your vote in each rank was
independent, except that you were not allowed to vote for more than
one rank for a candidate (they counted it as the higher expressed
rank, and they counted overvotes in an exclusive rank as no vote in
that rank, I think. I'm not sure about the exact details, and they
may have varied with jurisdiction.)
To my knowledge, this analysis of Bucklin as a sincere Range ballot,
confined to the approved ratings, is original, but perhaps someone
else has noticed it before me. It doesn't seem that obscure....
And then that holy grail, in a runoff system, becomes possible: a
system which satisfies not just the Majority Criterion, but the
Condorcet criterion as well, that seeks maximum approval, and that
will allow a Range winner to defeat a Condorcet winner -- but only in
a runoff, where the electorate explicitly makes that choice. To fully
do this requires doing three kinds of analysis on the Range ballots
feeding a Bucklin system, the most difficult being Condorcet
analysis. It's not necessary if there is a single-candidate majority
in the first rank, for sure. And it need not be full Condorcet
analysis, it merely need be a pairwise comparison with whomever might
otherwise win the election.
It's not hard to understand at all. But I'd rather see more interest
before starting to develop very specific proposed rules.
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