[EM] Real IRV Ranked Ballots
Steve Eppley
seppley at alumni.caltech.edu
Tue Mar 2 17:32:09 PST 2004
Hi,
Eric Gorr wrote:
> Through my efforts to get out there an advocate for both Approval
> and good Condorcet Methods (MAM, etc.), I am currently in
> communication with a dedicated IRV supporter who may be claiming
> that they would move away from IRV if a real example could be
> given where IRV selected an obviously wrong winner.
One of the reasons it may be hard to find real world
examples is the same reason it is hard to find real world
examples that show plurality rule selects poorly: Good
candidates choose not to compete, to avoid being spoilers
or because the voting method will "wrongly" defeat them, so
the votes tend not to reveal the problem.
Places that use IRV, like Australia and Ireland, also use
STV proportional representation alongside, so the party
elite have plenty of info from the voters to be able to
predict and avoid spoiling. Also, if my memory is correct
they don't use primary elections; the party elite decides
who will run, and they're smart enough not to run spoilers.
In Australia they can predict voter turnout too, since
voters are fined if they don't vote, so their estimates are
going to be pretty accurate.
See if the IRV supporter is receptive to the argument that,
if we switch to IRV, the parties will still only nominate
one candidate each to avoid spoiling, and we'll still have
only two parties with a chance to win. So the only effect
of that "reform" would be to make weak third party
candidates like Nader irrelevant, unless the third party is
foolish enough to run a stronger candidate who spoils and
helps elect their greater evil. What I want from voting
reform is more competition to be the best compromise, so we
can rank less-corrupt centrists over more-corrupt
centrists. IRV won't give us that kind of competition. It
tends to defeat centrists, so why would they bother to run?
You may recall that the Center for Voting & Democracy
didn't bother to advocate Instant Runoff until 1997,
claiming until then that no single-winner method is any
good and only proportional representation is a worthwhile
reform. At the end of 1996, they polled their membership
asking whether CV&D should also work for reform of single-
winner methods. Presumably their members said yes, since a
month later they came out for IRV. But their members
hadn't said to work for IRV, they said to work for a good
single-winner method, and this came after about a year of
people pointing out in their maillist that there are some
worthwhile single-winner voting methods. (Condorcetian
methods like TopCycle//Minmax(wv), not Instant Runoff.)
Check out what textbooks on Robert's Rules of Order (such
as Scott, Foresman) say about Instant Runoff. (They don't
call it Instant Runoff; they refer to it by the name
"preferential voting" even though that name is generic for
all preference order voting methods. But you can tell by
their description that they mean Instant Runoff.) They
point out how it often defeats the best compromise and
recommend against using Instant Runoff when better methods
are feasible. In their pre-computer age context, better
methods require people to assemble together so they can use
a multiround voting method: pairwise single-elimination
agenda voting, which chooses an alternative in the top
cycle. But their thinking is obsolete, since other better
methods have become feasible in large elections now that
voters can submit machine-readable preference orders.
(Perhaps the best of these Condorcetian methods is better
for assemblies than single-elimination agenda voting, too,
since there would be no agenda that could be manipulated,
and the sizes of majorities would make a difference.)
Here's a real world example: Suppose John McCain had run in
2000 against Bush & Gore in the general election. Most
Gore voters preferred McCain over Bush. Most Bush voters
preferred McCain over Gore. And a significant number of
voters thought McCain was best. So McCain would have been
a Condorcet winner, with large majorities over Gore and
Bush. But Instant Runoff would have eliminated him early,
since it is unkind to centrists.
> Naturally, I will be testing my movie survey results against IRV.
>
> In the meantime, they have stated:
>
> >I believe Ireland and Australia report full ranked
> >ballots.
>
> Can anyone verify this or submit any proof that it is not true?
Do they mean each voter expresses a strict ordering of the
alternatives, or do they mean that all the votes are
published after election day? I'd guess the former, which
won't be helpful. But maybe they've entered the computer
age by now, and aren't so corrupt that they'd prevent the
votes from being tallied unofficially by a variety of
voting methods.
> Also, wanted to thank Adam Tarr for providing the following
> two examples:
>
> 10% FarRight>Right>Centrist>Left>FarLeft
> 10% Right>FarRight>Centrist>Left>FarLeft
> 15% Right>Centrist>FarRight>Left>FarLeft
> 16% Centrist>Right>Left>FarRight>FarLeft
> 15% Centrist>Left>Right>FarLeft>FarRight
> 13% Left>Centrist>FarLeft>Right>FarRight
> 11% Left>FarLeft>Centrist>Right>FarRight
> 10% FarLeft>Left>Centrist>Right>FarRight
>
> 7% FarRight>Right>LuckyRight>ModerateRight>ModerateLeft
> 2% Right>FarRight>LuckyRight>ModerateRight>ModerateLeft
> 4% Right>LuckyRight>FarRight>ModerateRight>ModerateLeft
> 7% LuckyRight>ModerateRight>Right>ModerateLeft
> 15% ModerateRight>LuckyRight>ModerateLeft>Right
> 16% ModerateLeft>ModerateRight>LuckyRight>Left
> 15% ModerateLeft>Left>ModerateRight>FarLeft>LuckyRight
> 13% Left>ModerateLeft>FarLeft
> 11% Left>FarLeft>ModerateLeft
> 10% FarLeft>Left>ModerateLeft
>
> which I have been using extensively to provide IRV supporters
> evidence that IRV can fail rather dramatically in realistic cases.
> For the moment, none have been able to mount a defense for why IRV
> selects the winner it does. The current IRV supporter rejected the
> examples outright, calling the voters 'oddly split' and rejecting
> that examples such as these would ever occur.
Oddly split? The first example is consistent with placing
the voters along a one-dimensional "left-right" spectrum
that's nearly a classic bell-shaped curve:
16
15 16 15
15 16 15
13 15 16 15
13 15 16 15
11 13 15 16 15
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
10 11 13 15 16 15 10 10
Note that the columns at the far left & right could be
replaced with multiple smaller columns, to more closely
match a bell-shaped curve, without changing their
preference orders:
16
15 16 15
15 16 15
13 15 16 15
13 15 16 15
11 13 15 16 15
11 13 15 16 15 10
11 13 15 16 15 10
11 13 15 16 15 10
7 11 13 15 16 15 10 7
7 11 13 15 16 15 10 7
7 11 13 15 16 15 10 7
7 11 13 15 16 15 10 7
3 7 11 13 15 16 15 10 7 3
3 7 11 13 15 16 15 10 7 3
3 7 11 13 15 16 15 10 7 3
Here's an attempt to place the voters of the second example
on a 1-dimensional spectrum. At first glance it does look
oddly split, but spreading out some of the columns helps it
more closely match a bell-shaped curve:
16
15 16 15
15 16 15
13 15 16 15
13 15 16 15
11 13 15 16 15
10 11 13 15 16 15
10 11 13 15 16 15
10 11 13 15 16 15
10 11 13 15 16 15 7 7
10 11 13 15 16 15 7 7
10 11 13 15 16 15 7 7
10 11 13 15 16 15 7 4 7
10 11 13 15 16 15 7 4 7
10 11 13 15 16 15 7 4 2 7
10 11 13 15 16 15 7 4 2 7
16
15 16 15
15 16 15
13 15 16 15
13 15 16 15
11 13 15 16 15
11 13 15 16 15
11 13 15 16 15
11 13 15 16 15
7 11 13 15 16 15 7
7 11 13 15 16 15 7
7 11 13 15 16 15 7
7 11 13 15 16 15 7 4
7 11 13 15 16 15 7 4
2 7 11 13 15 16 15 7 4 2
1 2 7 11 13 15 16 15 7 4 2 1 1 1 1 1 1 1
Perhaps your friend was confused by votes like
Centrist>Right>Left>FarRight>FarLeft, which seem to ping-
pong between left & right. But that's exactly how a
centrist who is slightly right of center would see the
lesser alternatives.
> If anyone has more realistic examples where IRV selects
> an extremely poor winner, I would be interested.
On November 15 1998 I posted a simpler example which seems
pretty bad. I'm repeating it here:
* * *
Here's a 4-alternative IRV example for you to consider,
where IRV's failure & irrationality seem incontrovertable.
Horrid IRV example
------------------
34: A>B>C>D
15: B>A>C>D
15: B>C>A>D
10: C>B>D>A
10: C>D>B>A
16: D>C>B>A
(The numbers indicate percentages of the voters.)
This scenario seems quite plausible. Suppose A is a bit
"left", B is "centrist", C is "right", and D is "far right
fringe." We can expect A's supporters to vote mostly ABCD,
as shown. We can expect B's supporters to be somewhat
split between BACD and BCAD, as shown. We can expect C's
supporters to be somewhat split between CBDA and CDBA, as
shown. We can expect D's supporters to vote mostly DCBA,
as shown. It also makes sense to call B "centrist" since B
is the only candidate that doesn't have a majority of
voters on either side.
How does IRV tally this? It first eliminates D, since 16
first place votes is deemed weakest, and transfers those 16
ballots to C. Then it eliminates B, since B's 30 first
place votes is deemed weaker than C's 20 firsts plus 16
seconds and weaker than A's 34 firsts. Ultimately IRV
elects C.
Note that B has more first place votes than C, and more
second place votes than C, and more first+second place
votes than C. And of course, B trounces C pairwise (64% to
36%) and trounces all opponents pairwise. No matter how I
look at this, I can't see any reason to prefer electing C
more than B. The reason IRV elects C is purely an artifact
of the mindless procedure: it counts D's 16 for C before it
counts A's 34 for B, rewarding the fringe group, in order
to minimize the tally labor. Now that we can tally
elections by computer, there's no excuse for using IRV.
* * *
Here's a way to place those voters and the four candidates
on a curve that it approximately bell-shaped:
15 15
12 15 15
10 12 15 15 10 10
8 10 12 15 15 10 10 8
8 10 12 15 15 10 10 8 5
4 8 10 12 15 15 10 10 8 5 3
4 8 10 12 15 15 10 10 8 5 3
A B C D
Note that none of the counts in the Instant Runoff
iterations are close enough to tied to prevent you from
tweaking the voter percentages a little to make it even
more closely match a bell-shaped curve. For instance, you
could change a few of the B>C>A>D votes to C>B>D>A or
C>B>A>D without affecting the outcome, and B would still
have a huge majority over C.
Of course, you can simplify the example by removing D from
contention, and B still has a supermajority over C, yet C
still wins. But IRVings like to imagine that voters
intensely favor their top choice and are nearly indifferent
about the other alternatives (which is belied by the fact
that so much effort goes into defeating greater evils by
settling for compromises) so including D reduces the number
of voters who rank C first and thereby undermines their
claim that C ought to win. Also, including D helps show
IRV's mindless discrimination: the A faction's second
choices are never counted, whereas the D faction's second
choices are counted.
Bill Clark just added the following to this thread:
-snip-
> Suppose actual voter ratings are as follows:
>
> A:10,D:1 - 49%
> B:10,D:1 - 26%
> C:10,D:1 - 25%
>
> And the vote (which is merely ordinal) goes like this:
>
> A,D - 49%
> B,D - 26%
> C,D - 25%
>
> IRV: C is eliminated after the first round, then D is
> eliminated after the second round, and A ends up beating
> B in the third round.
> Condorcet: D wins.
A minor correction: IRV eliminates D first, then C, then B.
Yes, D would be a bad winner here (assuming the ratings for
candidates left unrated are zero, not some large negative
number). You could make the example even more stark by
changing the ratings of B & C from 10 to 2. But what seems
implausible is that candidates not shown who are much
better than D would not jump into the race, since it would
be so easy to beat D.
If there aren't such candidates, then this is one of many
cases where majority rule could theoretically let down the
passionate minority by deferring to a nearly indifferent
majority. The usual solution is vote trading. In this
case, A would attract additional support by making promises
to a few of the voters who would otherwise consider D
slightly better than A, and then A would become the
Condorcet winner.
--Steve
"Don't blame me; I voted for Kodos."
-- Homer Simpson (final line of "Citizen Kang")
More information about the Election-Methods
mailing list