The Value of First Choice Votes
By James Green-Armytage
One of the
most frequently raised objections to Condorcet on the part of IRV supporters is
that there can be a Condorcet winner with very few (or even zero!) first choice
votes.
But 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 Condorcet.
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 themselves.
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 method.
I will try to
structure this posting around four variations on an example.
In the
example, 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 variation to variation. That is, whatever a given voter's
opinion is of Bush in one variation, he has the exact same opinion of Bush in
all the variations. However a given voter feels about Nader in one variation,
his feeling is exactly the same in every other variation. And so on.
The only
difference between the variations 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 based on a
political spectrum where the electorate is distributed slightly more towards
the wing candidates then toward the center candidates.
Variation #1: Only Bush and Gore run
48: Bush > Gore
52: Gore > Bush
Variation #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)
Variation #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)
Variation #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 variations. 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 variations. That is the point:
*Voter sentiment is entirely constant from variation to variation*.
In all of
these variations, Gore is a clear Condorcet winner.
However, the
winner under IRV is variable. That is, using IRV, Bush wins variation #3.
Is this
justified? If so, how is it justified?
Is Gore a
turkey in variation #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 variation #2, where they all run? His first choice
support is the same (27), but he wins IRV there.
Is Gore a
turkey in variation #1 or #4, with 52% of the vote? No?
Well, the
voters don't like him any less in variation #3 or #2. None of them have a
lesser opinion of his leadership abilities or policies than they do in any of
the other variations. How, then, could he be a turkey in one variation, but not
the other?
Is Bush a
turkey candidate in variation #2? He only gets 21% of the vote there.
But does he
stop being a turkey in variation #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 variation than in the other, when the
actual voter opinion with regard to him is identical?
In the
variations 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, let’s 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 points
16%: Bush: 80 points,
Buchanan: 50 points, Gore: 30 points, Nader: 10 points
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 points
27%: Nader: 90 points,
Gore: 80 points, Bush: 30 points, Buchanan: 10 points
(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 variations. 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 variation
#2. And so on.
So, how does
any of this illustrate my point?
Again, I ask
whether it is justified that Bush wins variation #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 feeling, either.
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 (the question of the specific utility of the candidates to each voter)
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 (or, ranking him
as an insincere and ineffectual second choice.) 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.
I think that
voting systems that place especial value on first choice votes as IRV does do
not just reward candidates who have more intense core supporters. I think they
may also reward candidates whose general support base lack the imagination or
the awareness to reach for something better. A likely result of such systems is
that the standards for the representativeness of candidates won't improve much,
as their general supporters will be deterred from ranking a more favored
candidate for fear of their compromise candidate facing an early elimination.
Now, if you
like, we can go back to the classic 'turkey' example that some consider to be a
failure of Condorcet’s method.
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 the race?
49: A > B
51: B > A
Does B look
like a turkey now? Not at all.
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
X 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, and it is unlikely that people would report these numbers
honestly given a cardinal ratings system. So it is presumptuous to call B a
turkey just because s/he lacks first choice votes.
In
conclusion, no, I don’t believe that Condorcet is perfect. In particular, the
possibility for successful order reversal / burying strategies using Condorcet
methods are unsettling, and it is important to discuss in what ways this
problem can be dealt with.
What is not
interesting to discuss is the idea that Condorcet is a lousy 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 bogus.