[EM] the value of first choice votes
jarmyta at antioch-college.edu
Wed Jul 9 09:50:24 PDT 2003
David Gamble wrote:
>No I don't put the Condorcet "nightmare" in the same ballpark as the IRV
>"nightmare" I feel it is worse. I am not at all happy- for all sorts of
>"turkey" reasons explored extensively in previous posts- with any
>single member system that can elect candidates with a low first
I (James Green-Armytage) reply:
This seems to be one of the most frequently raised objections to
Condorcet on the part of IRV supporters: that there can be a Condorcet
winner with very few (or even zero!) first choice votes.
How important are first choice votes in and of themselves?
It is possible that this question is purely a "matter of personal
opinion", an unbridgeable gap, which no one will cross as a result of
rational argument. If so, then IRV supporters are destined to remain IRV
supporters no matter what, and Condorcet supporters are destined to prefer
But I'm not sure that this is really the case. Rather than just talking
around this issue, and assuming that there is no room for anyone to change
their opinion on it, I believe that it may be possible to talk about
exactly *why or why not* first choice votes are important in and of
I am, as I have mentioned, an ardent Condorcet fan. I will argue that
first choice votes have no particular meaning in and of themselves; that
their value is always ambiguous. The position of one candidate on a ballot
only acquires explicit meaning in relation to the position of another
candidate. Hence the indispensable value of the pairwise comparison
But I will emphasize that it is not only because I am a Condorcet fan
that I argue this. I am a Condorcet fan in the first place because I
believe it is true.
I will try to structure this posting around a series of examples. I
imagine four candidates: George Bush, Al Gore, Ralph Nader, and Pat
Buchanan. I will imagine that Gore is left, Nader is far left, Bush is
right, and Buchanan is far right.
I will imagine that the feelings of any given voter about any given
candidate do not change *at all* from example to example. That is,
whatever a given voter's opinion is of Bush in one example, he has the
exact same opinion of Bush in all the examples. However a given voter
feels about Nader in one example, his feeling is exactly the same in every
other example. And so on.
The only difference between the examples is the presence or absence of
different candidates in the running. That is, specifically, the presence
or absence of Ralph Nader and Pat Buchanan. Therefore, it probably makes
more sense to imagine this not as a series of sequential elections, but as
different possible outcomes of a single election given different possible
sets of candidates running.
Please note that there is nothing freakishly unlikely about this example
(use of real names aside). It is a fairly straightforward four person
election where the electorate is distributed slightly more towards the
wing candidates then toward the center candidates.
Example #1: Only Bush and Gore run
Example #2: Bush, Gore, Buchanan, and Nader all run.
27: Buchanan, Bush, Gore, Nader
(27 total Buchanan first)
16: Bush, Buchanan, Gore, Nader
5: Bush, Gore, Buchanan, Nader
(21 total Bush first)
6: Gore, Bush, Nader, Buchanan
19: Gore, Nader, Bush, Buchanan
(25 total Gore first)
27: Nader, Gore, Bush, Buchanan
(27 total Nader first)
Example #3: Bush, Gore, and Nader run.
48: Bush, Gore, Nader
(48 total Bush first)
6: Gore, Bush, Nader
19: Gore, Nader, Bush
(25 total Gore first)
27: Nader, Gore, Bush
(27 total Nader first)
Example #4: Buchanan, Bush, and Gore run.
27: Buchanan, Bush, Gore
(27 total Buchanan first)
16: Bush, Buchanan, Gore
5: Bush, Gore, Buchanan
(21 total Bush first)
52: Gore, Bush, Buchanan
(52 total Gore first)
These are the four examples. Please note that they are entirely
consistent with each other. The complete preference rankings are given in
#2, where all the candidates run. These preference rankings, minus the
candidates not running, will exactly produce the preference rankings in
the other examples. That is the point: *Voter sentiment is entirely
constant from example to example*.
In all of these examples, Gore is a clear Condorcet winner.
However, the winner under IRV is variable. That is, using IRV, Bush wins
Is this justified? If so, how is it justified?
Is Gore a turkey in example #3? Does he not have enough "strong support"
to deserve to win? Well, he did only get 25 first choice votes, whereas
Bush and Nader got 48 and 27. Does that prove that he doesn't have as much
"strong support" as Bush, because he has fewer first choice votes? Hmm...
On the other hand, is Gore a turkey in example #2, where they all run?
His first choice support is the same (27), but he wins IRV there.
Is Gore a turkey in example #1 or #4, with 52% of the vote? No?
Well, the voters don't like him any less in example #3 or #2. None of
them have a lesser opinion of his leadership abilities or policies than
they do in any of the other examples. How, then, could he be a turkey in
one example, but not the other?
Is Bush a turkey candidate in example #2? He only gets 21% of the vote
But does he stop being a turkey in example #3, in which Buchanan is not
running, and in which he wins? Why? Those 27% of voters who prefer
Buchanan don't change their opinion about Bush at all; they don't like him
any more or less. How could you say that Bush has stronger support in one
example than in the other, when the actual voter opinion with regard to
him is identical?
In the examples where Buchanan does not run, then Bush may seem to have
more core supporters than Gore, that is, voters who will rank him first
no matter what. But when Buchanan runs, it becomes clear that that is not
the case. So, it is a false assumption that someone who ranks a candidate
first is necessarily a core supporter of that candidate.
In order to illustrate my point a little bit more completely, lets
imagine that we can take a poll and get each of the voters to sincerely
rank the candidates on a scale from 0 to 100, in terms of how much they
like them, etc. Here is the (imaginary) result:
27%: Buchanan: 90 points, Bush: 80 points, Gore: 30 points, Nader: 10
16%: Bush: 80 points, Buchanan: 50 points, Gore: 30 points, Nader: 10
5%: Bush: 80 points, Gore: 30 points, Buchanan: 20 points, Nader: 10 points
6%: Gore: 80 points, Bush: 30 points, Nader: 20 points, Buchanan: 10 points
19%: Gore: 80 points, Nader: 50 points, Bush: 30 points, Buchanan: 10
27%: Nader: 90 points, Gore: 80 points, Bush: 30 points, Buchanan: 10
(Of course the uniformity of voter opinion in this example is
unrealistic, but that is irrelevant. A more varied set of ratings would
take up vastly more space and still produce the same results.)
Note that the scores given here are entirely consistent with all four
examples. That is, the 19% who give Gore 80 points, Nader 50 points, Bush
30 points, and Buchanan 10 points, are the same 19% who voted Gore, Nader,
Bush, Buchanan in example #2. And so on.
So, how does any of this illustrate my point?
Again, I ask whether it is justified that Bush wins example #3 using IRV.
52% of the voters give Gore 80 points and Bush 30 points. 48% of the
voters give Bush 80 points and Gore 30 points.
Why oh why, then, does Bush ever deserve to beat Gore? You can't make an
argument by saying that more voters prefer Bush to Gore, of course. My
point is that you can't make an argument on the grounds of intensity of
Let me say something about those who rank Nader first and Gore second...
27% of the voters rate Gore at 80 points and Nader at 90 points.
25% of the voters rate Gore at 80 points and Nader at 50 points.
Critics of Condorcet seem to assume that if a voter lists someone as
their second choice, then they necessarily like that candidate less than a
voter who lists him/her as their first choice. But this is not necessarily
true! It is quite possible, as in my example, that they just happen to
like someone else more. Since this question cannot be answered by any
realistically manipulation-resistant voting method, I submit that it is
irrelevant in public elections. What is relevant is the result of a
pairwise contest. This is because it can be made relatively clear that a
voter prefers Gore to Bush, but it cannot be made clear *how much* any
voter compares Gore to Bush.
In this case, and other cases like it, IRV is giving the 27% Nader-Gore
voters a strong incentive to vote insincerely by leaving Nader off the
ballot. This kind of incentive may often lead to having fewer viable
candidates in the field, less competition as well as less precision, and
therefore less accountability and lower standards. I am very unhappy with
IRV's asking people to bury their sincere favorite as an acid test of
"strong support" for a compromise candidate.
Now, if you like, we can go back to the classic 'turkey' example that I
have seen a number of times on the list.
49%: A, B, C
2%: B, A, C
1%: B, C, A
48%: C, B, A
B is the Condorcet winner, of course, and A wins IRV. B may look like a
turkey to some people here, but what would he look like if C withdrew from
Does he look like a turkey now? No!
Conversely, candidates A or C might suddenly have far fewer first choice
votes if a similar candidate to them entered the race. In general, for any
candidate A who has a large number of first choice votes, there is always
the possibility that another candidate X could enter the race, such that
most of the people who would have voted for A first would now vote for X
first and A second. There is no way of knowing from the results of a
ranked ballot whether such a candidate S exists or not. And, whether this
happens or not, it doesn't say anything about the strength of voter
preference in terms of the relationship between A and the other candidates
in the field.
Given the classic turkey example, critics of Condorcet seem to assume
that the sincere 0-100 candidate ratings would look something like this:
49%: A 90 points, B 30 points, C 20 points
2%: B 90 points, A 80 points, C 70 points
1%: B 90 points, A 80 points, C 70 points
48%: C 90 points, B 30 points, A 20 points
But as far as anyone knows, they could actually look like this:
49%: A 90 points, B 80 points, C 20 points
2%: B 90 points, A 50 points, C 40 points
1%: B 90 points, C 50 points, A 40 points
48%: C 90 points, B 80 points, C 20 points
In the second example here, who cares if B is only the first choice of 3%
of the candidates? 100% of the voters give B 80 points or higher, which is
something that you can't say about A or C, who are each rated down at 20
points by nearly half of the electorate.
The point is that you really can't tell. Both of these examples look
exactly the same on a ranked ballot. So it is presumptuous to call B a
turkey just because s/he lacks first choice votes.
In conclusion, no, I dont believe that Condorcet is perfect,
specifically because of the universality of strategic incentives in
multi-candidate races. I concede that Condorcet can produce incentives for
truncation and order reversal, and I concede that examples of such are not
freakishly rare. I would probably argue that plurality, Approval and IRV
produce significantly nastier strategy incentives on a more frequent
basis, but that is at least an interesting idea to debate.
What is not an interesting idea to debate is whether Condorcet is a
crappy method because it allows candidates to win without lots of first
choice votes. That objection to Condorcet, as I hope I have helped to
demonstrate, is totally bogus.
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