[EM] Our Standards & Condorcet contd.
dfb at bbs.cruzio.com
Sun Mar 24 13:24:41 PST 1996
Let me demonstrate this with an example. A much more reasonable
& un-contrived example than the ones in the anti-Condorcet paper:
Voters' sincere preferences:
40%: Dole, Clinton, Nader
35%: Nader, Clinton, Dole
[The Clinton voters have no 2nd choice listed for simplicity, & because
it wouldn't matter under realistic conditions anyway, & because in
this 3-candidate race they have no reason to vote a 2nd choice, &
because it will matter later when I discuss an _implausible_ eventuality]
If voters vote complete & sincere rankings, Clinton wins by Condorcet
& by Copeland. The difference between those 2 methods isn't tested here,
since there's no circular tie to solve. Clinton beats Dole 60-40, &
Clinton beats Nader 65-35.
Now say the Dole voters "truncate", or "bullet-vote", and don't
rank Clinton. This could be done strategically, but will be quite
commonly done without any strategic intentions. Here are the resulting
35%: Nader, Clinton
Now we have a "circular tie", in which the Dole voters have allowed
Nader to beat Clinton 35-25. The other pairwise results are as above.
Nader beats Clinton beats Dole beats Nader. A circular tie.
Alright then who's least beaten by Condorcet's rule? Well the
Dole voters can't do anything about the fact that Dole has a
majority against him, a 60-40 majority. Nore can the Dole voters'
truncation change the fact that there is no majority against
Clinton. Clinton only has the smaller of the 2 extremes against
him, 35%. Dole has 60% against him, and Nader has 40% against
him. Clinton wins. The Condorcet winner who'd beat each one of
the others in separate 1-on-1 elections wins.
Now, you may at some point hear someone express concerns about
"order-reversal", so let's try it in this example. Let's say the
Dole voters attempt order-reversal strategy, in order to make
Clinton very beaten, hoping that will help Dole:
40%: Dole, Nader
35%: Nader, Clinton
This time the Dole voters have caused Clinton to be beaten 75-25.
As before, the Dole voters can't do anything about the fact that
Dole has a majority against him, a 60% majority.
But another thing the Dole voters can't do anything about is the
fact that Nader _doesn't_ have a majority against him. The Dole
voters, since they don't constitute a majority (Dole couldn't
lose if they did) don't have the power, on their own, to make
someone be beaten by a majority. They only did it to Clinton with
the help of the Nader voters. But no one's helping them do it to
Therefore, there's not a thing the Dole voters can do to keep
Nader from winning. Well there's 1 thing they can do: They can
avoid the fruitless risky order-reversal attempt.
Notice that all it took to punish the order-reversal, to make it
impossible for it to succeed, was for the Clinton voters to not
vote a 2nd choice, or at least to not vote for Dole. But it wasn't
even necessary for the Clinton voters to know which side would
be the big side with the capability of trying order-reversal--
merely not voting a 2nd choice completely thwarts any order-reversal
So then, that's the defensive strategy against order-reversal:
Don't vote for the candidate of the likely order-reverser. In general,
don't vote for anyone you like less than the likely Condorcet winner.
In a 3-candidate race, there's no reason for the Clinton voters to
vote a 2nd choice anyway. In a larger election, more candidates, it
could be uncertain who's Condorcet winner, but all voters have access
to the same strategic information, and the Dole voters know that.
So the mere fact that other voters even _might_ expect the possibility
of order-reversal, and vote accordingly, is enough to deter the order-
I re-emphasize that this won't happen anyway. Bruce & I have agreed
that the devious strategy of order-reversal won't be tried in a public
election on a scale sufficient to change the election result.
Sorry about going into such detail about something that won't happen.
Now, what would Copeland do in the 2 above cases, where the Dole
voters truncated, and where they order-reversed?
Well, first of all, Copeland is always completely indecisive in a
3-candidate race, and relies completely on a tie-breaker. Bruce
proposes, in his Regular-Champion method, that Condorcet use
Plurality as its tie-breaker. So what would happen?
In both circular tie examples, Regular Champion's Plurality tie-breaker
would pick Dole. If we want something better than Plurality, the above
example would suggest that we need somethng better than Copeland or
Regular-Champion, to paraphrase something that was recently said to
Our goal in single-winner reform can be summarized by saying that
we want to get rid of the need for defensive strategy to the greatest
A group of voters consisting of a full majority of all the voters has
the power to make happen whatever they want to. Easy enough if they
all vote the same candidate in 1st place, but not so easy if what they
all agree on is that they want to defeat a certain candidate. They
can always do it, always get what they all agree on wanting, but
with most methods, including Copeland, that will often require
"defensive strategy": They'll need to voter other than sincerely.
I define "defensive strategy", then, as the need for a full-majority
group of voters to vote other than sincerely to get a result that
they all want.
The need for defensive strategy is to be minimized, and is to be
completely gotten rid of when possible.
The above 2 paragaraphs summarize what we want in a single-winner
method. We could call that the "Defensive Strategy Standard", or
we could call it the "Generalized Majority Standard". I'm calling
That standard is a general statement of what we'd all like. It isn't
the kind of simple yes/no test to apply to a method, the kind of
thing mathematicians like, so I'm calling it a standard, rather than
a criterion. But that standard still has a definite meaning, and
specifics can be added.
For instance, since, as I showed, Condorcet won't ever elect someone
with a majority against him under plausible conditions where the
result matters, that means that Condorcet is completely free of
defensive strategy need under those conditions.
I showed, in the 3-candidate example, how easily it is to thwart
order-reversal, in the highly implausible scenario where it's a
possibility. The fact is that, in Condorcet, a group consisting
of a majority not only has the power to make someone have a majority
against him, but also has the power to make anyone else _not_
have a majority against them (simply by not helping vote anyone
over him). This means that, simply by voting a short ranking,
a ranking that doesn't include a particular candidate, a full
majority who rank someone over him have the power to ensure that
he can't win.
Summarizing that paragraph, a full majority have the power, in
Condorcet, to ensure the defeat of any candidate without using
any strategy other than a short ranking. They don't need
to use the insincere voting strategies of voting anyone else
equal to or over their favorite. No need for defensive strategy
involving order-reversal or insincerely ranking 2 candidates equal.
Now, because the real world isn't always as neat as voting-system
reform advocates would like it to be, I have to say that, if there
are lots of candidates, and if the cheating voters have impossibly
accurate & complete predictive informtion, and are very improbably
sophisticated additionally, then they could contrive to create
a circular tie among the candidates whom they're voting over
the Condorcet winner, and, if they're impossibly lucky & well-
informed, could create a combination of their votes with the
votes of those canddiates' supporters that would cause all
those candidates to be have majorities against them.
Forget it. It's impossible. But a mathematician would object
that the fact that that can be mentioned, even in principle,
should prevent me from saying that Condorcet guarantees that
it's _never_ necessary for a group consisting of a full majority
to use use order-reversal or insincerely rank candidates equal
in order to get a result that they all want. Sorry, mathematicians,
I'm saying it anyway.
Aside from that, it's also true that adding a simple refinement
to Condorcet would make the impossible-in-practice offensive strategy
in the previous paragraph impossible-in-principle too:
When A beats B beat C beats A, that's called a circular tie if
these are the only alternatives, or the ones that beat all the
others. But in general, it's called a "cycle". It's possible for
one element of a cycle to be a cycle. In other words, it's possible
for a cycle to be an element of a cycle. Such a cycle that is an
element of another cycle can be called a "subcycle".
So we simply add this rule: Subcyles shall be solved by Condorcet's
rule before solving a cycle that they're part of. The winne in the
subcycle shall take that subcycle's place in the cycle that the
subcycle is part of.
In other words, we start with by solving the highest-order subcycles
by Condorcet's rule. We than replace that subcycle by its winner, in
the cycle of which the subcycle was an element.
Now someone might object that that's too complicated to propose
to the public. Here are 3 answers to that:
1. It won't be needed anyway, since the kind of offensive strategy
that it would make impossible-in-principle is already
2. If some voters were sophisiticated enough to attempt order-reversal,
then others would be sophisticated enough to know about it to, and
would be open to suggestions on how to thwart it, and would be
interested enough to listen to the subcycle rule.
3. The subcycle rule isn't really complicated, and its wording
can probably be improved.
One last thing about order-reversal, it should be obvious that it
the Dole voters, for instance were organized to order-referse, this
would take lots of public communication about it, and it would
be quite impossible to keep this information from the other
voters, who could easily use easy non-devious, non-insincere
counermeasure against it (not ranking Dole). So the reversal
would backfire & elect Nader.
And even aside from everything said so far about order-reversal,
the fact that it could only work if its victims voted for the
perpeterators' candidate makes it a particularly dastardly
betrayal. If it were attempted even once by Republican voters,
whether it succeeded or not (& I've shown why it wouldn't),
the intended victims of the order-reversal would never again
rank a Republican candidate.
All in all, then, order-reversal is not a problem in Condorcet,
though I readily admit that it could be a problem in Copeland.
Sorry about the amount of detail, but that's what it takes
when detailed criticism is possible. I had to cover the topic
so as not to be accused of leaving something out, in the
Condorcet vs Copeland debate.
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