[EM] Condorcet - let's move ahead
SEppley at alumni.caltech.edu
Sat Jan 17 19:40:35 PST 2009
[I'm not subscribed to RangeVoting at yahoogroups.com, so I won't see
replies posted only there.]
On 1/9/09 Dave Ketchum wrote:
> Extended now to EM - I should have started this in both.
> On Fri, 09 Jan 2009 15:40:58 -0000 Bruce R. Gilson wrote:
>> --- In RangeVoting at yahoogroups.com, Dave Ketchum <davek at ...> wrote:
>>> We need to sort thru the possibilities of going with Condorcet. I
>>> Method must be open - starting with the N*N matrix being available
>>> to anyone who wants to check and review in detail.
>>> If the matrix shows a CW, that CW better get to win.
>>> Cycle resolution also better be simple to do. We need to debate
>>> what we document and do here such as basing our work on margins or
>>> vote counts.
>> Yes. My biggest gripe with Condorcet is that cycle resolution in many
>> systems is so complex that it does not seem that a typical voter (as
>> opposed to people like us who are personally interested in electoral
>> systems) could understand what is being done.
I think there's no need to gripe or fret. Resolving cycles doesn't need
to be complex. Here are 2 solutions.
1) The "Maximize Affirmed Majorities" voting method (MAM) is an
excellent Condorcet method and is very natural. Here's a simple way to
explain how it works and why:
The basis of the majority rule principle is that the more people there
are who think candidate A is better than candidate B, the more likely
it is that A will be better than B for society. (Regardless of whether
they think A is best.)
Since majorities can conflict like "rock paper scissors" (as shown
example that follows) the majority rule principle suggests such
should be resolved in favor of the larger majorities.
Example: Suppose there are 3 candidates: Rock, Paper and Scissors.
Suppose there are 9 voters, who each rank the candidates from best
to worst (top to bottom):
* _4_ _3_ _2_
Rock Scissors Paper
Scissors Paper Rock
Paper Rock Scissors**
7 voters (a majority) rank Scissors over Paper.
6 voters (a majority) rank Rock over Scissors.
5 voters (a majority) rank Paper over Rock.
By paying attention first to the larger majorities--Scissors over
then Rock over Scissors--we establish that Scissors finishes over Paper
and then that Rock finishes over Scissors:
It can be seen at a glance that Rock also finishes over Paper.
The smaller majority who rank Paper over Rock are outweighed.
Since Rock finishes over both Scissors and Paper, we elect Rock.
I think that's not too complex. (How did anyone reach the dubious
conclusion that beatpaths or clone-proof Schwarz sequential dropping
will be easier than MAM to explain?) I think the only operational
concept that will take work to explain is that there is more than one
majority when there are more than two alternatives. (Analogous to a
round robin tournament, common to all Condorcet methods, and not really
hard to explain.) Most people already know what an order of finish is,
and I think most people are familiar enough with orderings that they
will recognize the transitive property of orderings when it's presented
Jargon terms such as "Condorcet winner," "beats pairwise" and "winning
votes" are unnecessary. Their use may interfere with moving ahead.
Top-to-bottom orderings are more intuitive than the left-to-right
orientation many other writers use in their examples. Two common
meanings of "top" are "best" and "favorite." Two common meanings of
"bottom" are "worst" and "least favored." In those contexts, "over"
means "better" or "more preferred." Left-to-right offers no such
friendly connotations (except to the "leftist" minority, and the
opposite to the "rightist" minority). Left-to-right becomes even worse
when symbols like the "greater than" sign (>) are used, since a lot of
people are repelled by math symbols. Left-to-right rankings may
interfere with moving ahead.
2) One could promote the variation of Instant Runoff (IRV) that allows
candidates to withdraw from contention after the votes are published.
(I'm not suggesting eliminating the secret ballot. The corresponding
voters' identities would not be published.) The withdrawal option
mitigates the spoiling problem of plain IRV. It reduces incentives for
voters to misrepresent preferences (true also for Condorcet methods, but
I think not true for Range Voting, Approval or Borda). I expect
IRV+Withdrawal would exhibit a solid Condorcetian tendency to elect
within the sincere top cycle, since supporters of spoilers would
pressure them to withdraw when needed to defeat their "greater evil."
Obviously, its promotion could leverage the efforts of the promoters of
plain IRV. It can even be argued that IRV+Withdrawal satisfies the
spirit of the Later No Harm criterion, if people (or courts) care about
Assuming IRV+Withdrawal were employed by society for many elections, the
eventual switch to a Condorcet method like MAM (or MAM+Withdrawal) would
either be found to be unnecessary, or would become fairly obvious due to
observations of candidates' occasionally ignoring their supporters'
pressure to withdraw (or to not withdraw).
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