[EM] The Hippopotamus Logic

[Steve Eppley]

Donald D wrote:
>Mike:
>>>>If a full majority of all the voters indicate that they'd rather
>>>>have A than B, then if we choose A or B, it should be A.
>>>>
>>>>Condorcet's method is the only proposed method [that] respects that
>>>>principle, meaning that it will never unnecessarily violate it.

>Donald:
>>>Would you show me an example of IRO violating the rule of majority?

>Steve: 
>>The 46/20/34 example shows IRO violating it.  We've discussed this
>>already, but here goes again:
>>   46:ABC
>>   20:B
>>   34:CBA
>>A majority (54) indicated they'd rather elect B than A, yet IRO
>>elects A.  If there's some principle which makes you think this
>>is a "necessary" violation, I'd like to hear it.

>Donald: 
>Candidate B does not have fifty-four votes. Candidate B only has
>twenty votes - it is right there in your example in black and white
>20:B

I didn't write that B has 54 votes; I wrote that 54 voters indicated
they prefer B more than A.  This is a primary atttribute of the 
ballots cast, not a secondary "hippo" attribute like "votes".
This is derived from the definition of ranked ballots, not from 
the choice of tally algorithm.  You've ignored the 34 who voted 
they prefer B more than A, even though they're right there in 
black and white:  34:CBA  

You used hippo logic when you claimed B has only 20 votes.  No matter 
what tally method is used, there are 54 voters whose ballots indicate 
they prefer B more than A.  

>Candidate A has forty-six votes and candidate C has thirty-four
>votes - there is a difference between votes and selections - this
>is suppose to be an example of a Instant-Run-off election - not
>Condorcet.

You're using hippo logic to ignore the voted preferences which you 
find inconvenient to your argument.  Go back to the basic majority
rule principle, which doesn't specify Condorcet's method:
  (Candidate IDs A & B switched here to avoid confusion)
  If a full majority of all the voters indicate that they'd rather
  have B than A, then if we choose A or B, it should be B.

What's your rationale for ignoring the 34 who indicated they'd
rather have B than A?  Hopefully you have a better answer than
the hippo-ish "they should be ignored because IR ignores them."

>When you say "A majority (54) indicated they'd rather elect B than
>A .." you are creating a STANDARD. Now the question is: How was this
>standard created - answer: you used Condorcet.

I don't agree.  I simply didn't ignore the 34 who voted they prefer
B more than A, since their preferences are trivially obvious to the
most casual observer of their ballots.

You do ignore those 34 preferences.  Let's try to stick with 
fundamentals: why should the 34 be ignored?

If you want to advocate a principle which most voters will accept as
reasonable, your answer should be consistent with the reality that
most voters, in plurality practice, demonstrate their willingness 
to vote against the greater evil rather than waste their votes on
favorites who can't win.  People like the 34 want their votes
counted against their greater evil A, not wasted on C.

Another "pairwise" principle is that if there's a candidate who would
defeat any of the others in a runoff then this is the one who should
be elected.  But there are plenty of pairwise methods, like Copeland,
which satisfy this but which I don't advocate.  If anything, you
should be targeting a herd of pairwise hippos, and not use overly
specific language against just the one critter (Condorcet) which 
most EM poll responders support.

-snip-
>When we compare apples to oranges we cannot use the apple nor the
>orange as a standard to compare each. That would be like saying:
>Condoret is best because Condorcet is more like Condorcet than any
>other method - this is more of the Hippopotamus logic.

I think you're really saying it would be like "Condorcet is best 
because Condorcet is more like Pairwise than any other" and this 
doesn't make much sense.

I believe I'm saying that the tally method shouldn't ignore the
voters' preferences, that this is an important principle, and that
Condorcet's method satisfies this principle best, much better than 
IR and better than the other pairwise methods.

Are you saying that the 34 who prefer B to A *should* be ignored? 
If so, Instant Runoff is the method for you.  But if so, why so?

>This example you have presented is not the worst example used to
>support Condorcet but it is bad on three accounts.
>   One: It is loaded to favor one candidate
>   Two: It is not realistic
> Three: These election votes would not come from a Instant-Run-off 
>          election.
>
>This example is loaded to favor candidate B with more than twice
>the number of selections over either of the other two candidates -
>when we consider only the first two selections. The first two are
>the only selections of any importance with a three candidate race.
>You have given 46 selections to candidate A - you have given 34
>selections to candidate C - BUT! you  have given 100 selections 
>to candidate B - and then you state that B should be the winner -
>surprise! - surprise!

Your argument seems very weak:  

First, you can add 20 selections to A and C by changing the 20B to
10BA 10BC.  And you can downsize B's numbers further to close the gap
more.  And you're arbitrarily looking at the top two selections of 
each voter; why not one or three?

Second, and more important, B is such a broadly supported compromise
that your "surprise!s" are actually a sarcastic way of saying the
opposite of their literal meaning: "it's NO surprise that B is
elected since B is such a good candidate; of course B should be
elected."  The "surprise" is that someone who claims to be a 
reformer would advocate a method which wouldn't elect such a good 
candidate. 

I see nothing wrong with "loading" an example to favor the
compromise candidate in order to demonstrate such a fundamental
failure of IR to elect the compromise who would beat any of the
candidates in a runoff.  Examples are supposed to test methods.
This is the most basic test of methods, if one accepts the principle
that the compromise candidate ought to win a single-winner election.  
If you don't accept this principle, I'd like you to say so clearly,
so I can insert it into the SW Commentary when I account for the 
lone supporter of IR as basing his opinion on nonacceptance of a
principle which I anticipate most readers will accept.

You don't need to rely on my opinion of this principle, known
academically as the Condorcet Winner criterion.  Try asking Instant
Runoff "advocates" like Rob Ritchie for their views on it.  He'll 
tell you that Condorcet is technically superior to Instant Runoff, 
and that he talks about Instant Runoff because he thinks IR is 
quicker to explain when he's describing how to end the LOE dilemma,
and because he thinks single-winner reform isn't very important 
compared to prop rep.  (It would be nice if he'd defer to the people 
who seriously promote single-winner reform for cues on how to 
properly describe it).

>The second way in which this example is bad is that you have the 
>46 voters of candidate A voting lockstep all for the same candidate
>B on the second selection. Likewise you have the 34 voters of
>candidate C doing the same. This is not realistic. This would 
>never happen. 

This is an unimportant criticism.  I know you have a preference 
for complex examples which obscure the principle they're trying 
to illustrate, but that doesn't mean the simple example doesn't
illustrate the principle, nor that a complex "realistic" example
can't demonstrate the principle.  See below for a more realistic 
example that ought to satisfy you on this (non)issue.

>I do not know how these voters would vote their second selections
>but I am going to split them in half so I can get on with my side
>of this discussion. 23AB  23AC   20B 17CA  17CB

An even split by wing voters is contrived and unrealistic, and
leads to an example which doesn't prove anything one way or the
other since it carelessly fails to generate results where IR and
Condorcet differ.  It's a waste of time to look at examples where 
the results are the same.  It's a good use of time to look at 
examples where results differ, and study why they differ and the 
implications of the difference.

What would be more realistic is a very uneven split by wing voters.
In a partisan election--where single-winner reform is most crucial-- 
very few voters of a wing would prefer a candidate of the opposite
wing more than the candidate of the center.

Try something more realistic like this, not a scenario where so many 
voters are so unrealistically confused about which candidate is 
furthest from their position:
   39AB  <-- for most wing supporters, middle is realistic 2nd choice
    4AC  <-- these aren't lockstep
   20B     <--- (these split below, be patient)
    5CA  <-- these aren't lockstep
   32CB  <-- for most wing supporters, middle is realistic 2nd choice

Maybe you're more interested in two-dimensional examples, which 
are more complicated than the 1-D we've been mainly dealing with.  
Perhaps you think that the principles demonstrated by 1-D examples 
don't apply when the number of issue spectra is increased.  They
do, but the construction of good examples is more tedious and their 
analysis is messier, and ascii text is not as optimal as graphics 
to illustrate the 2-D voter distributions and candidate positionings.
Still, we should probably try this at least once since there are 
groups like the Libertarians who would split more evenly in their 
second choices.

>This is getting better but this is not the votes from an
>Instant-Run-off election - which is the third bad thing about your
>example. The voters of the last place candidate in the polls would
>not omit making a second selection in an Instant-Run-off election.
>So - I am going to give second selections to the twenty votes of
>candidate B and I am going to split these selections evenly between
>A and C - just to be fair. 23AB  23AC  10BA  10BC 17CA  17CB

A good point.  But the truncation by the 20 isn't an essential part
of the example, and supplying second choices for them doesn't save 
IR in a realistic example:
   39AB
    4AC
   10BA    <--+-- even split, to be close to realistic
   10BC    <--'
    5CA
   32CB

>Now this is an example of an Instant-Run-off election that would
>"mollify" even me. Under run-off rules candidate A is still the
>winner. 

Examples (like anecdotes) don't prove things; "counterexamples"
disprove them.  The claim you make is that IR is better than 
Condorcet.  The claim I make is that Condorcet is better than IR.
To disprove your claim I provide an example where Condorcet elects 
a "better" candidate than IR.  To disprove my claim what you should 
be looking for is an example where IR elects a "better" candidate
than Condorcet, where "better" is evaluated according to some
defensible principles or criteria which you don't leave unstated.  
I think the closest you've gotten to that is if I read between the
lines and assume your principle is related to "the 34 who prefer B
more than A *ought* to be ignored", since that would at least give us
an example where IR is claimed to elect a "better" candidate.  But it
doesn't yet give us an explanation why you think that's a reasonable
principle.

Tally the realistic set of ballots I've supplied, or explain 
why they still don't seem realistic to you.  (Maybe not enough 
Libertarians?  We'll need to show more than 3 candidates.)
   39AB
    4AC
   10BA
   10BC
    5CA
   32CB

   IR:        eliminates B (20); then A wins (53).
   Pairwise:  B>A (52>48) and B>C (59>41).  B wins.

It's a good example of a good example :-) since the methods being
compared produce different results.  Now we have to decide which
result is better:

If it's desirable that the winner represent the voters for whom
s/he's the first choice, then A is the better winner since A
maximizes the number of voters who got their first choice. 
(Plurality does a wonderful job satisfying this dubious principle,
so IR has some single-winner company.)  It's an excellent principle 
for prop rep, which can represent people with their first choices
without wasting many votes.  (Pure proxy PR adheres most closely 
to this principle.) 

But if it's desirable that the single winner represent all the
voters (i.e., is a centrist) then B is the better winner.

If you want to argue that A is not a horrible winner here, you're
going to have a tough row to hoe.  Electing the beats-all winner is
pretty much universally agreed to be an crucial principle, even by
other Instant Runoff advocates.

>If someone were to show me your example and ask me: "What can you
>say about this election by only seeing and knowing this first tally
>of the votes?" I can tell a few things about the example by just
>looking at it.
>   One: The election was not an Instant-Run-off election
>   Two: The election is going to use Condorcet as the single-winner
>          method
> Three: This is the first time that these voters voted in a
>          Condorcet election.
>I can make these three statements because one group of voters
>refused to make any more than one selection. They are being clever.
>This is the way to manipulate a Condorcet election - have your
>group refuse to support any other candidates on the second selection
>- but you hope the other voters will support your candidate on their
>second selections. Sometimes it will work - you may be able to pull
>it off - your candidate may win it all.

You haven't fully understood the uses of the truncation tactic, and
I guess we Condorcet advocates are to blame for this by overusing
examples where the middle voters truncate.  Maybe we should use 
this example when debunking IR:  
   35 XYZ 
   16 YXZ 
   16 YZX 
   33 ZYX
   IR:       eliminates Y, elects X.
   pairwise: Y>X (65>35)  Y>Z (67>33)   Y trounces all; Y wins.

The middle voters' truncation in most of the examples is a defensive 
tactic which protects the election of the middle candidate.  Somehow 
you've gotten the idea that the tactic would also be useful for 
wing voters, even though the examples have demonstrated the 
opposite.  

The middle voters only "need" to truncate if they believe that wing
voters are going to engage in tactics on a scale large enough to
steal the election.  Under normal circumstances, they can freely 
vote their sincere preferences, even when they're not actually
indifferent.  

Look at my realistic example where all voters supply a second 
choice.  Pairwise methods elect B, the best winner, and IR 
elects A.

If middle is a beats-all candidate and other voters haven't engaged
in misrepresentation massive enough to change the result, middle
still wins.  This is a basic scenario methods need to satisfy: the
"sincere beats-all" candidate deserves methods' special protection.

If there's a sincere circular tie, picking one as the "best" winner
isn't as important.  Some EM subscribers even have a preference for
Smith//Random to express this belief.

Truncation succeeds at defending the middle but doesn't help a 
wing steal the election when wing voters try it, using Condorcet.

>When the next election for this race comes around more of the
>voters will be clever. The votes of the next election may look like
>the following:
>          40A  2AB  4AC  20B  30C  2CA  2CB

>Candidate B no longer has 100 selections - candidate B is now a
>loser - like he should have been at the start of this example.

It's totally unrealistic to think that voters dominated by the desire 
to vote against the greater evil would sit back and let the greater 
evil win rather than rank the middle second.  (Someone who claims 
others' examples are unrealistic should try harder to be realistic
himself.)  The 30C votes are too contrived to make a good example;
they'd vote 30CB.  (Or even 30BC, if that's what's needed to defeat 
their greater evil A.  The reason I'm interested in single-winner 
reform is so that voters won't have to vote insincerely in order to
defeat the greater evil, because this is the force which produces a
two-party system in single-winner elections.  What's your reason?)

You correctly pointed out that with IR the 20 middle supporters would
provide a second choice, knowing their first choice would be
eliminated.  But now you incorrectly state that in Condorcet wing
voters would rank only one choice.  You're incorrectly assuming that
a truncation tactic which succeeds at defending a middle candidate
has some value for wing voters.  It doesn't--if they neglect to 
rank the middle compromise they're running the risk of electing 
the greater evil of the opposite wing, with nothing to gain by 
the tactical attempt.

>The people have the right to know before an election which
>single-winner method will be used to crunch the numbers because the
>selections in a Condorcet election are different from the selections
>in an Instant-Run-off election. 

I absolutely agree.  The people would need to know that they still
have to deal with the LOE dilemma in IR, contrary to the promises of
the "reformers" who sold them on the system, and plan their unhappy
votes accordingly.  Which is how I felt Tuesday using vote-for-one
plurality:  ;-(

And potential candidates would need to know that if they enter an IR
race, they can fragment the first choice votes of their supporters
and not necessarily get the transfers.  IR is still highly sensitive
to the Spoilers problem: 
   39AB                           39AB
    4AC                            4A
   10BA             or            10BA
   10BC                           10B
    5CA                            5A
   32CB                           32B
   IR: A wins.                    IR: B wins.
Realistically, candidate C would prefer B is elected rather than A.
Will candidate C decide not to run rather than risk B losing to A?
Is this any way to promote multiparty democracy?

And candidates who did choose to run in an IR race would need to know
that they shold avoid the centrist position, since this would allow 
left-of-center and right-of-center candidates to grab away most of 
the first choices.  (See the recent messages on spatial analysis of 
IR.)  Let's spin the mandates a bit, hmm?

>The selections have different weights and meanings. In Condorcet
>the selections are votes and can be used against the voters' first
>selection - in Instant-Run-off only the first selection has a vote.

You omitted: In IR, the voter's preference for the lesser evil over
the greater evil might not be used against the greater evil.  

This is far more likely to occur in IR than a preference for a
lesser evil over a greater evil acting against one's favorite in
Condorcet.  And in IR the defeated "lesser evil" may be a compromise 
candidate who would beat all the others in runoffs, whereas in 
Condorcet the "problem" is in a less important scenario, a circular 
tie where the voters are so divided that even //Random would be a 
reasonable tie-breaker.

Whether it's IR or Condorcet which reformers campaign for, the
voters are going to be told that their lower-ranked selections will
be counted, not ignored, in the tally.  For IR this claim is a lie;
it's only true for the tiny fringes whose candidates figure to be 
eliminated right away.  For the important candidates at and near 
the center, it's going to be a mess for the voters.

>As more people know about the Condorcet method most of them will
>only make one selection. The Condorcet election becomes a plurality
>election - the more things change the more they remain the same.

This is the same mistake as above, where you incorrectly assume 
that a tactic that works to defend the middle compromise is also of
benefit to either of the wings.

>Instant-Run-off does not have this problem. As people understand
>the method they will see that it is to their advantage to make more
>than one selection. 

Condorcet doesn't have this imagined problem.  Not only will people
understand the advantage of voting more than one selection, they'll
also understand the advantage of voting sincerely.  Even the middle
voters will for the most part rank other candidates below the
middle, and you can substitute 10BA 10BC for 20B in all the examples
except where the middle voters are tactically defending against
massive tactics by a wing. 

Perhaps if you look at a 5-candidate example it will help you
understand trucation better.  For simplicity assume there's a
dominant spectrum on which the 5 candidates and most voters can 
be evenly placed, and ignore the rest.
   L2 > L1 > M     <-- voters who are far left of center
   L1 > L2=M       <-- somewhat left of center
   M               <-- centrists
   R1 > R2=M       <-- somewhat right of center
   R2 > R1 > M     <-- far right of center

The point I'm beginning to illustrate is that when there's a 
candidate (M) who would beat all other candidates if matched in a 
runoff, then, if the method is Condorcet:
  1. Voters can lose by not extending their selections at least 
    as far as M--a greater evil could be elected.
  2. Voters don't help M nor candidates they prefer more than M 
    by explicitly ranking candidates they prefer less than M.
  3. Voters gain protection of M against other voters' possible
    misrepresentation tactics by not explicitly ranking any 
    candidates below M. 

The middle voters, realistically, will vote more like 
   M > L1=R1 > L2=R2
and realistically this won't harm them, but the clever ones will
consider applying these principles.  Especially if they learn that
other voters seek to massively misrepresent to try to defeat M.
(Look at #3.)

These principles apply to all the voters, not just the middle
voters.  But a 3-candidate example is too small to show the
application of these principles except for the middle voters. 
If you put the principles together, you'll see that except for the
middle voters, voters don't gain by ranking only a first choice; 
the farther from the middle, the more selections would be made by 
the very clever voter.  

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)