[EM] Condorcet - let's move ahead

Steve Eppley SEppley at alumni.caltech.edu
Sun Jan 18 12:50:54 PST 2009


On 1/18/2009 10:52 AM, Dave Ketchum wrote:
> Your promotion of IRV discourages for, while its ballots would be valid
> Condorcet ballots, its way of counting sometimes fails to award the
> deserved winner (even when there is no cycle making the problem more 
> complex).

I do not promote IRV.  IRV+Withdrawal is not IRV.  The withdrawal option 
allows candidates to correct for IRV's tendency to undermine centrist 
compromise.  Candidates would have the incentive to withdraw because 
they and their supporters would prefer centrist compromises over 
"greater evils."  See the example below.

> That the indicated winner could withdraw does not really help, for that
> candidate does not necessarily know whether IRV has erred.

I don't see why Dave wrote about the "indicated winner" withdrawing.  
The point of withdrawal is to allow *spoilers* to withdraw after the 
votes are cast.

Also, it would quickly become clear whether IRV has "erred."  The votes 
would be published soon after the election day polls close.  Then the 
candidates would be given days after the votes are published to decide 
whether to withdraw.  During that period of time, the candidates (and 
other interested people) can download the published votes and privately 
tally who will win if no one withdraws and who will win if they and/or 
other candidates do withdraw.

Here's an example to illustrate.  Suppose there are 3 candidates: Left, 
Center and Right.  Suppose the voters vote as follows:

     40%         5%          10%         45%
     Left        Center      Center      Right
     Center      Left        Right       Center
     Right       Right       Left        Left

When the votes are published, everyone can see that IRV will elect Right 
if no one withdraws, and will elect Center if Left withdraws.  Since 
Left and Left's supporters prefer Center over Right, Left has a strong 
incentive to withdraw, electing the Condorcet winner.

Left is not the "indicated winner."  The only way Left could win is if 
both Center and Right withdraw or do not run, which would be crazy.  
Left is just a spoiler.  If Left didn't compete, Center would win 
outright with 55% of the votes (neglecting the effect of possible 
changes in voter turnout).

> Therefore I still wait to hear from others as to whether MAM deserves
> backing, though it properly handled your simple cycle example.

MAM satisfies all the desirable criteria satisfied by Beatpath Winner 
(aka Cloneproof Schwartz Sequential Dropping--CSSD for short--aka 
Schulze's method).  It also satisfies some criteria that Beatpath Winner 
fails: Immunity from Majority Complaints (IMC, which is satisfied only 
by MAM), Immunity from 2nd-Place Complaints (I2C) and Local Independence 
of Irrelevant Alternatives (LIIA).  Furthermore, simulations by several 
people have shown that over the long run, more voters rank MAM winners 
over Beatpath winners than vice versa, and a majority rank the MAM 
winner over the Beatpath winner more frequently than a majority rank the 
Beatpath winner over the MAM winner. (Those simulations suggest MAM 
comes a little closer than Beatpath Winner to satisfying Arrow's 
Independence of Irrelevant Alternatives criterion.)  See 
www.alumni.caltech.edu/~seppley for more information about MAM and 
criteria it satisfies or fails.

An alternate description of MAM is to find the order of finish that 
minimizes the size of the largest "thwarted" majority, where a thwarted 
majority is defined as a majority who ranked x over y when the order of 
finish does not rank x over y.  It's been proved that the 2 different 
descriptions of MAM are equivalent.  I'm mentioning this alternate 
description just in case there are some people who will find it easier 
to understand.  I prefer describing MAM in terms of constructing the 
order of finish a piece at a time by considering the majorities one at a 
time from largest to smallest, since I think more people will understand 
it and that's how MAM is actually implemented in software. (It's 
computationally much quicker than finding the best order of finish by 
comparing all possible orders of finish.)

As far as I can tell, the reason some groups have adopted Beatpath 
Winner rather than MAM is because there used to be a website co-written 
by Mike Ossipoff in which he claimed it will be easier to explain CSSD 
than MAM. (Mike used the name Ranked Pairs instead of MAM, but he 
definitely meant MAM, not the pairwise margins-based voting method that 
Nicolaus Tideman invented and named Ranked Pairs in 1987/1989.)  Mike 
based his conclusion on a few personal anecdotes, which I think can be 
attributed to his own greater familiarity with the Schwartz set that 
made him more comfortable explaining in terms of subsets of candidates. 
(I could forward emails from Mike where he acknowledges MAM is at least 
as good as Beatpath Winner.)  As my previous message about the ease of 
explaining MAM illustrated, Mike was mistaken about which is easier to 
explain.  Judge for yourselves.

> On Sat, 17 Jan 2009 19:40:35 -0800 Steve Eppley wrote:
> > Hi,
> >
> > [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
> >>>> claim:
> >>>>
> >>>> 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.
> >>
> > -snip-
> >
> > 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
> > in the
> >      example that follows) the majority rule principle suggests such
> > conflicts
> >      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
> > Paper,
> >      then Rock over Scissors--we establish that Scissors finishes 
> over Paper
> >      and then that Rock finishes over Scissors:
> >
> >         Rock
> >         Scissors
> >         Paper
> >
> >      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
> > visually.
> >
> > 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
> > that.
> >
> > 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).
> >
> > Best wishes,
> > Steve

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