[EM] The Hippopotamus Logic

Mike Ossipoff dfb at bbs.cruzio.com
Wed Nov 6 18:25:29 PST 1996

donald at mich.com writes:
> Dear List, the following exchange of messages took place:
> 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
> 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 Condercet.

Whoa, Don: No one said that B had 54 1st choice votes. You aren't
paying attention, so let me recount the discussion for you:

1. I said that only Condorcet will never unnecessarily violate
the basic democratic principle that if a full majority indicate
that they'd rather have A than B, and if we choose A or B, then
it should be "A.

2. You asked for an example of IRO failing that principle.

3. Steve gave an example in which A wins, even though a majority
have indicated that they'd rather have B than A, but where
no majority has indicated that they'd rather have something
instead of B. So IRO in that example has unnecessarily violated
that principle.

4. You've somehow changed the subject to 1st choice votes.
You can try to deny that that basic democratic principle is 
important, but you can't say that IRO doesn't violate it in
that example.

> 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

No. I'm stating an already existing standard or principle. Majority
rule. Not violating majority wishes.

> created - answer: you used Condorcet. You used Condorcet to create a
> standard in which you used to compare Instant-Run-off. The next step is to
> compare Condorcet to this "Standard" - and Condorcet should meet the
> standard - surprise! surprise!

This has already been explained to you, but, because of your tendency
to talk without listening, you still seem to miss it: Condorcet was
chosen because it meets that & related standards. 

No one used Condorcet to "create" the majority rule standard.

You're all confused, and you've got your causation all backwards.

> You cannot do this Steve. We've discussed this already, but here goes
> again. 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.

As Steve's example shows, IRO violates majority rule in a way that
could never happen with Condorcet. 

You're verbatim repeating your "apples & oranges" & "hippopotamus"
wordings. We're not comparing Condorcet to IRO using Condorcet, we're
comparing them by the majority rule standard.

> 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

I don't suppose you could justify that claim, could you? 
Loaded in the sense that the middle candidate has fewest 1st
choice votes? It's been demonstrated that that can happen even
with a bell-shaped 1st distribution of voters on the political

Or, look at it this way. For a middle candidate who is the smallest
to be Condorcet winner, with a majority over each of the others, all
that's necessary is that he/she be bigger than than the difference
between the other 2. A sufficient, but not necessary condition for
this is that all 3 candidates be within a factor of 2 of eachother.

And, in general, there's a chance in 3 that the middle candidate
is the smallest, if we don't assume any particular distribution.

Besides, if you think that the example is loaded because MIddle
is smallest, because that's the only time when IRO fails, then
I remind you that if Middle isn't smallest then Plurality does't
have a strategy dilemma either. Plurality doesn't have a problem
when IRO doesn't. But IRO has one when Plurality doesn't. What
we want is a method that works even when Plurality doesn't.

>    Two: It is not realistic

Justify that claim too, if you can. Why is the example unrealisitic?
Steve demonstrated that Middle can easily have fewest 1st choice

>  Three: These election votes would not come from a Instant-Run-off election.

Are you saying that peole wouoldn't vote sincerely if they knew that
the count would be by IRO? I agree with you. There would be a tendency
for the C voters, in that example, to insincerely vote B in 1st place,
to strategically avoid election of majority-rejected A. That, Don,
is a need that we want to avoid.

> 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!

Then why are you so surprised? I have no idea what the hell you're talking
about when you say the example gives 100 selections to B, unless
you're referring to the fact that, since B is between A & C, and
C voters consider B closer to C than A is, and A voters considser B
closer to A than C is, therefore A voters rank B over C, and C voters
rank B over A. 

> 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.

As I've explained to you more than once, it isn't "lockstep", it's
the fact that B is between A & C. B is closer to A than C is, and
B is closer to C than A is. Do you understand that yet??

Do you know of any Progressives, Nader voters, or would-be Nader
voters, who say that Dole is better than Nader? No, actually most
people you talk to who'd like to vote for Nader are voting for
Clinton instead (lockstep?) because Clinton's policies are
somewhat closer to those preferred by the progressives. Whether
Clinton is enough closer to justify voting for him is something
I disagree on, but he's acknoledged as the middle of those 3, and
that's why the progressives are voting for him. Not "lockstep", but
common knowledge about position & policies.

> This is not realistic. This would never happen. I do not know how these

Nonsense. It happened yesterday. People who prefer an extreme voted
to elect Middle, and they did it uniformly, not in "lockstep", but
because of common knowledge about position & policies, as I just

> 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

Nonsense. That's absurdly unrealistic.
In the political elections that we're concerned about there's
a compromise, and there's a lesser-of-2-evils problem because of
a perceived need to make that compromise beat someone worse. I
shouldn't have to still be explaining that to you. In your example
there isn't a compromise. Just 3 sets of voters who are indifferent
or equally-divided about a 2nd choice. That isn't an example where
there'd be a LO2E problem. IRO does have a LO2E problem under
more realistic conditions. And your example isn't one that tests
IRO'ss ability to abide by majority rule, and no doubt that's
why you like that example.

> 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

Fine, so now the B voters, instead of being indifferent, are equally
divided. But the implausible part, and the part that makes your
example irrelevant to the LO2E question, and which makes it not
a test of IRO's majority rule ability, is the equal division of
A & C voters regarding their 2nd choice. Sure, you can find an
example where IRO _won't_ violate majority rule. I never meant to
imply otherwise. But that doesn't change the fact that, under
ordinary conditions, IRO is the method with the much greater 
tendency to violate majority rule.

> 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. Just for the
> fun of it - let us see who wins using Condorcet.
>                     A and B           A and C          B and C
>                     Pairing           Pairing          Pairing
> 23AB                23A               23A              23B
> 23AC                23A               23A                  23C
>      10BA               10B           10A              10B
>      10BC               10B               10C          10B
>           17CA      17A                   17C              17C
>           17CB          17B               17C              17C
> --------------      --------          -------          -------
> 46A  20B  34C       63A 37B           56A 44C          43B 57C
> Look at these results! - A beats B and C  Surprise! Surprise!

Not really surprising.

> Candidate A is the winner. Candidate B is last - same as Instant-Run-off.
> Seems like when the example is realistic and not loaded the Condorcet
> results become the same as Instant-Run-off - the more things change the
> more they remain the same.

Yes, when the example is chosen by you, then it's an exmple where
there's no recongnized compromise, no LO2E problem to avoid, and
where IRO happens to not violate majority rule. The fact that
you can find an example where IRO doesn't violate majority rule
doesn't change the fact that IRO is a notorious violator of majority

> 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.

You mean because the B voters didn't vote a 2nd choice. Under
conditions of expected devioius voting, Middle voters indeed wouldn't
vote a 2nd choice. They have no need to anyway, with Condorcet's
method, since, unless extreme has an outright majority, one of
the extremes needs middle as a compromise. But avoiding the
voting of a 2nd choice is a defensive strategy that B voters would
only need under devious electorate conditions. In IRO they'd
have no need for such a strategy, because it wouldn't do them
any good: When their candidate has fewest 1st choice votes, then
there's nothing they can do to save him, except to hope that
one of the extremes will resort to lesser-of-2-evils voting.
That's like saying your tv is better than mine because you
don't adust a horizontal hold, because your tv isn't provided
with one.

>    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

As I said that's a defensive strategy to protect Middle under
devious voting condition. But I doubt very much that that's the
reason why B voters didn't vote a 2nd choice in Steve's exsample.
Most likely it's because it wouldn't have made any difference.
That seems to have missed you, even though I've often spelled it
out in my examples: "For simplicity the Clinton voters haven't
voted a 2nd choice. It wouldn't have affected the results if they

> will support your candidate on their second selections. Sometinmes it will
> work - you may be able to pull it off - your candidate may win it all.

"It all" being the election? One of the extremes needs Middle, unless
an extreme has a 1st choice majority.

> 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.

Should have been? Only if the C voters are idiot enough to not realize
that they might well need B as a compromise, since C can't beat A.

Don, as I've explained so many times, no method can protect voters
who are too stupid to vote for a compromise that they need. No
method could help C voters if they're unwilling to vote for that

No, there's no incentive for C voters to truncate. For 1 thing,
knowing that C may well be unable to beat A, they know they need
to vote for B in 2nd place. In fact, even if they believed that
C could beat A, there would still be no motive for C voters to
truncate. Condorcet is "truncation-resistant", meaning that
truncation can never gain the elecdtion of a candidate over
whom a majority have ranked the Condorcet winner.

In your example, the truncation by C voters has given the
election to A. Because of that truncation, A beats B &
C pairwise. Had the A voters ranked B in 2nd place, then
B would beat C pairwise, but that wouldn't affect A's
win; A would still beat B & C pairwise, and would therefore
win by Condorcet's method. So A, too, has no strategic
incentive to truncate.

> 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. The selections have different weights and meanings. In Condorcet

Yes, you've caught onto that have you? The fact that IRO & Condorcet
often give different results?

> the selections are votes and can be used against the voters' first
> selection - in Instant-Run-off only the first selection has a vote.

The only time when someone could regret a 2nd choice vote in Condorcet
would be if the B voters ranked A 2nd, and the A voters insincerely
ranked C over B. Order-reversal. As I said, under conditions where
that devious order-reversal strategy is likely, the defensive strategy
of the B voters is to not vote a 2nd choice, or at least to avoid
voting a 2nd choice for a candidate whose voters are likely to use
order-reversal against B. But the fact that the B voters know
that order-reversal might happen, and the facxt that they might
be defending against it, would deter the order-reversal. We've
already been all over this, when I discussed it with you a long
time ago. Just refer to my earlier letters about it. I likened
it to a game of "chicken", in which the B voters have the advantage
over potential order-reversers, because the order-reversers stand
to lose more.

Anyway, order-reversal is unlikely to occur on a scale sufficient
to change the election result. If it were likely to it would be
defended against, and only a fool would then try it.

> 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.

You've got it backwards, Don. There's no incentive for the A &
C voters to truncate, and in fact there's strong incentive for
the C voters to not truncate. In a Plurality election the C voters
would have to choose between a sincere vote for C & a lesser-of-2-
evils vote for B. In Condorcet, they can do both, vote sincerely
& protect B from A. In IRO, under plausible conditions (but maybe
not in examples chosen by you), the C voters will often have the
same LO2E dilemma as under Plurlity. And for the same reason:
They are only permitted to have a vote on 1 candidate at a time,
and are not permitted to have all their preferences counted when
it matters. Things indeed would stay the same if we adopted IRO.

> This is the big hurdle that Condorcet most likely can not get over - if
> people refuse to make a second selection the Condorcet method goes down the
> tube.

As I said, if people who need the compromise are too idiot to vote
for it, then no method can help them. Condorcet doesn't give an
incentive to not vote a 2nd choice. Your claim that it does
is an example of your Instant-Runoff-At-The-Mouth, without
regard to whether what you're saying is nonsense.

> Now you could have a law passed forcing people to make the required
> selections under fear that a Condorcet Technocrat will use a big RED marker
> to void their ballot.

Don't be an ass. You know that no one has proposed compulsory complete
rankings. In fact I've often pointed out that one reason why Condorcet
is better than other pairwise methods, such as Regular Champion, is
that there will predictably be much truncation in any rank-balloting
election, including a pulbic one. I'd never vote for all the
candidates. Though the Condorcet's method doesn't give strategic
incentive to truncate, there's such a thing as principle, and
principled truncation will often take place. I've called the
C voters who need B & don't vote for him idiots, but that's not
true if they absolutely reject B on principle. But if they truncate
on princple, then they, like me, would do so regardless of the method,
Condorcet, IRO, or whatever. That's irrelevant to the strategy issue,
the LO2E issue, or the majority-rule issue.

> 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.

IRO has the problem that defensive order-reversal is often needed:
A C voter in Steve's example (but not in your special IRO-friendly
example) would have strategic need to vote B in 1st place instead
of C.

> Donald,

> .-


More information about the Election-Methods mailing list