[EM] Bad Condorcet winners?

Bart Ingles bartman at netgate.net
Sun Mar 18 09:59:16 PST 2001


A couple of quick comments:

Tom Ruen wrote:
> 
> Mike, there are 2 ways to look at this. I chose the first, and you the
> second...
> 
> The question we're considering is "Which is simpler for voters to rank - IRV
> or Condorcet?"
> 
> 1. IRV is less demanding because it never uses lower rankings on a ballot
> until all higher candidates are eliminated. Therefore voters don't have to
> think very hard about lower choices. However when an election is a close
> 3-way contest, there is the dilemma on whether to compromise first to be
> safe against a strong scary candidate.

Actually, it doesn't need to be a particularly close 3-way contest.  The
no-show/non-monotonicity example I posted on March 10 was fairly close
between the 2nd- and 3rd place candidates (based on first-round totals),
but the 1st-place candidate had a considerable lead initially.

One gauge of how often order-reversal strategy would be needed (with IRV
or FPP) is to find out how often Condorcet winners are rejected when
everyone votes sincerely.  Merrill's (1988) computer models, based on
reasonably realistic spatial models, show Condorcet failures with IRV
about 5 or 6% of the time with three candidates, increasing
approximately linearly to around 32 or 33% of the time with seven
candidates (with no sign of leveling off).

This seems to say that in a race with seven candidates, approximately
1/3 of the voters would be better off voting for a lesser-evil candidate
as a first choice.  Although this also assumes that everyone has
complete info on the other voters, and is willing to compromise on the
Condorcet winner -- if not, then the same utility-maximizing strategy
considerations advanced for Condorcet and Approval come into play
(probably involving truncation strategy, which may also make some of the
order reversals unnecessary).

It gets even worse if the candidates "bunch together" with similar
policy positions.  In the same Merrill study, if the candidates tended
to deviate only half as much from the median position as the voters did,
Condorcet failures (and the need for insincere strategy) was around 30%
in 3-candidate races, to over 75% with seven candidates.

Runoff was essentially the same as IRV.  Of course, FPP is worse -- you
can add about 20% to the Runoff/IRV figures.

Bart



> 2. Condorcet is less demanding because voters never need to vote insincerely
> to get what they want. There is no spoiler candidate. Condorcet gives
> majority rule power in all dimensions. However this added power of ranks
> means voters must consider more.
> 
> What I am concerned about is whether in the end voters really WANT what they
> GET out of Condorcet.
> 
> I'm NOT worried about telling the person who is already offering a
> compromise vote (in Plurality) because they're afraid their favorite can't
> win. Those are the voters that will most benefit from approval or rankings.
> 
> I am worried that people who already are happy with a favorite in plurality
> who may somewhat thoughtlessly vote for a compromise in Condorcet simply for
> being a compromise.
> 
> If a voter looks at an election and sees 3 choices - Favorite, Compromise,
> and Opposite, I don't want voters to quickly rank "1.F 2.C 3.O" blindly
> because it seems "logical". I want voters to say, "After my favorite, who do
> I really think will make a better leader - Compromise or Opposite?" If,
> after serious thought, the voter says, "Yes, I would certainly rather have
> Compromise over Opposite", then I'm fully content.
> 
> However I expect in some cases voters will vote Opposite over Compromise.
> And I expect some voters to say "If this is my choice, I support neither."
> And that is a choice too and it means don't rank either!
> 
> This is a new responsibility voters have never had to consider before. For
> those that don't choose to think in detail about all those choices, my claim
> is they (and we all) are better off if they don't rank below their favorite
> or favorites.
> 
> My concern is that compromise candidates are the ones who have the most to
> gain by such negligent voting. The example: AC=49, BC=48, CB=3. This is an
> extreme example, but it forms the basis of my analysis. I'm willing to
> accept victory for a weakly-top-ranked candidate like C ASSUMING voters were
> thoughtful and want this compromise.
> 
> This is the entire basis of my concern. Bullet voting has a certain degree
> of power and voters are used to that. Voters who want more power can take it
> in Condorcet. I just want this power used wisely.
> 
> I am being protective of voters. I would rather they be conservative. If
> asked between two undesirable choices, sometimes it is better to just not
> answer if you're unsure. If they would not compromise in Plurality, no clear
> need to start in Condorcet.
> 
> That's my approach and that's my defense for Condorcet. Condorcet gives new
> power (more power than IRV), but doesn't require people take that power.
> That's good!
> 
> Tom Ruen
> 
> >
> > >
> > >These dilemmas show where Condorcet is more demanding on voters than IRV.
> > >IRV will never look at second choices for voters of A and C.
> >
> > What? How does that make IRV less demanding? When IRV ignores your
> > preference for Gore over Bush, because you sincerely voted Nader
> > 1st, and your Gore>Bush vote never gets counted because your traveling
> vote
> > hadn't reached Gore in time to save him from elimination--how do you call
> > that less demanding?
> >
> > Tom, you IRVies have it backwards. It's because you don't listen.
> > So I'm going to explain it to you again.
> 
> >
> > The whole purpose of rank balloting is so that you can help a compromise.
> > You or I may have no respect for that compromise, and
> > no intention of helping him. Irrelevant. Most people desperately need
> > to help the compromise. In case they might need him, it's important
> > to them to help him against a greater evil.
> >
> > Condorcet automatically lets the lesser-of-2-evils progressive fully
> > protect Gore against Bush, fully oppose Bush, without any insincere
> > voting. And that's what you call more demanding. IRV will often make
> > it necessary for that voter to insincerely rank Gore in 1st place, over
> > Nader, in order to keep Bush from winnning. And that's what you call
> > less demanding.
> >
> > >
> > >I believe in Condorcet process only given voter think well about lower
> > >choices
> >
> > If people don't care about their lesser choices, then no one,
> > including you IRVies, has reason to propose rank balloting.
> >
> > We need Condorcet or Approval partly because so many progressive voters
> > who dislike the Democrats  "think well" enough about them to dump
> > their favorite in order to help the Democrat, just as they'll often
> > have to with IRV.
> >
> > , or bullet vote if they're unsure what they really want. I'd rather
> > >voters be conservative than vote haphazardly on lower ranks.
> >
> > When progressives vote conservatively & cautiously, they help a
> > lesser-evil, at any cost to their favorite. I don't know what you
> > mean by "vote haphazardly". Rank sincerely?
> >
> >
> > >Ranking many
> > >choices sincerely is a great responsibility!
> >
> > Nonsense. Sincere ranking is the easiest and least demanding form
> > of voting. That's the advantage of Condorcet. Condorcet is the method
> > that, under plausible conditions, is free of need for strategy.
> >
> > You want responsibility? Be the person who calculates strategy for IRV.
> > I don't know that anyone has waded into that problem yet. It would
> > be horrendously complicated.
> >
> > Mike Ossipoff
> >
> >
> > _________________________________________________________________
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