[EM] More on JITW (was Re: Circular Stand-Off)

[Steve Eppley]

Markus Schulze wrote (in a message I nearly missed 
since I don't read all the EM messages):
> Dear Steve,
-snip-
> You will have to explain why you think that JITW is an
> improvement. When you write that "there is no 'correct' 
> candidate to withdraw (or to elect) when there is a sincere 
> circular tie," you admit that JITW doesn't lead to a "better" 
> election result than every other Smith Criterion election 
> method (since every candidate of the top set is equally 
> qualified). 

No, what I said (or meant to say) is that every candidate of 
the *sincere* top cycle is equally qualified.

What we want is to elect a member of the sincere top cycle, 
not a "voted" top cycle which may include the "less qualified" 
candidate of a faction voting strategically, plus a patsy 
candidate which the reversers insincerely ranked ahead of one 
or more of the sincere top cycle.

Simply satisfying the Top Cycle criterion isn't enough to 
distinguish a strategically voted top cycle from the sincere 
one, as far as I know.  But the patsy may have an incentive 
to withdraw, and if this withdrawal is allowed by JITW this 
would elect one of the sincere top cycle.

* *

I don't think that JITW will be needed with a good method like 
TopCycle//Condorcet(VotesAgainst) or Schulze's method.  I'm 
not advocating JITW at this point for use with such methods, 
only for use with IRV where IRV is being pushed.  

The main purpose of JITW is to mitigate the flaw of 
Instant Runoff, by using JITW//IRV.  IRV does not satisfy 
the Top Cycle (Smith) criterion, and can easily defeat the 
entire top cycle.  So I wonder whether Markus (and others)
would agree that JITW//IRV is better than IRV.  (Mike Ossipoff 
has agreed.)

An important element of the JITW proposal is that the voters' 
orders of preference will be published.  (This won't be a 
violation of the secret ballot, since no information which 
could identify how any individual voted would be published.)  
Without the orders of preference, how can we tell empirically 
when IRV fails to elect one of the top cycle?  I would hope 
that IRV initiatives would require the publishing (on the 
internet) of the voters' orders of preferences, but I expect 
those advocates would be afraid of empirical evidence.  
Certainly CV&D hasn't shown any willingness to recommend 
that preference order voting initiatives mandate the 
publishing of the preference orders.

I don't think order reversal will be significant in public 
elections; it's truncation which methods need to deter or 
withstand.  Top cycle methods which are already highly-
resistant to truncation wouldn't need JITW.

I would propose JITW for use with a good top cycle method 
in the future, in the following circumstances:

  1. Order reversal is perceived to be a significant problem,
     empirically, after the adoption of the top cycle method.
  2. Order reversal is predicted to be a significant problem,
     theoretically, and thereby deters adoption of the
     top cycle method.
  3. Alternatives are still deterred from competing for fear
     of spoiling, in spite of the top cycle method making
     spoiling rare.

> And the claim that JITW guarantees that no candidate 
> will regret having competed, is simply not true. 
> 
> Example: JITW//Smith//Condorcet[EM] is used.
>    A:B=48:52
>    A:C=53:47
>    A:D=43:57
>    A:E=44:56
>    B:C=45:55
>    B:D=42:58
>    B:E=62:38
>    C:D=54:46
>    C:E=41:59
>    D:E=40:60
>    A, B, and C won't withdraw under any circumstances.
>    Candidate D prefers B to C to E to A.
>    Candidate E prefers C to B to D to A.
> 
> If no candidate withdraws, candidate A is elected.
> If only candidate D withdraws, candidate B is elected.
> If only candidate E withdraws, candidate C is elected.
> If both candidates, D and E, withdraw, candidate A is elected.

I acknowledge that the guarantee of no regret isn't ironclad.  
But it's still an important argument.  Markus had to concoct 
an unrealistic example in which all three of A, B, and C will, 
for unstated reasons, never withdraw.

I think Markus missed the point; there's a more important 
point than that (almost) no one will regret having run.  
Consider the effect of JITW on potential candidates when 
they are deciding whether to run, and on parties when they are 
deciding whether to nominate additional candidates for an 
office.  What they do at that time is more important than what 
they feel after the election.  What will they do at that time? 
Will they predict they will almost certainly not regret 
running, and therefore decide to compete?  Or will they fear 
there's a significant chance they'll regret running, and so 
decide not to compete?  If candidates are quite confident they 
won't be spoilers, they are more likely to choose to compete.  
An example like Markus' wouldn't deter people from competing, 
since it isn't plausible.

I withdraw my claim that JITW guarantees candidates will never 
regret competing, and substitute the more important claim:  

   With JITW, rational potential candidates will not be
   deterred by a fear of spoiling from competing.

I should have expressed it this way to begin with, but then 
Markus wouldn't have disproved the ironclad guarantee.  :-)

* *

I should have posted replies to comments about JITW months 
ago.  I wrote quite a lot I'd intended to post, but I didn't 
complete those messages.

When I first mentioned JITW last year, the only reply was from 
Demorep, who misunderstood the example I posted.  He thought 
that I meant C would withdraw in order to foil the reversal, 
and asked how can C know the votes were insincere?  But if he 
rereads the message he'll see I never said that the ACB votes 
were definitely reversals.  (I placed a '?' alongside them.)  
The reason I provided why C would choose to withdraw was 
not because C would want to foil the reversal but because 
C's preferences are presumably similar to the preferences 
of the C voters, who mostly prefer B to A.

After I brought up JITW again months later, there was a reply 
by Donald Davison, who claimed JITW would produce more 
corruption.  Davison claimed, in his rude way, that I was 
being unrealistic by not considering that candidates could be 
bribed to withdraw.  But in fact I had considered that, and 
I've also considered, unlike Davison apparently, that in any 
system candidates can also be bribed to withdraw before 
election day, or bribed to sabotage their own campaigns.  
That would produce an outcome no worse than if the bribery 
occurs after the voting.  Maybe this happens all the time; 
it's hard to tell if gaffes are intentional...

Davison's example requires 2/3 of the top cycle to be corrupt. 
(This is a situation in which a nonJITW topcycle method would 
be expected to elect a corrupt winner 2/3 of the time, and 
other methods would also tend to elect corrupt winners.)  
With JITW and/or a good top cycle method, I don't consider 2/3 
to be realistic, since noncorrupt candidates won't be deterred 
from competing because their fear of spoiling has been 
removed.  If we believe that voters will tend to rank the 
noncorrupt ahead of the corrupt, corrupt candidates will have 
a tough time reaching the top cycle.  

It's unclear whether Davison understood that a candidate 
bribed to withdraw would be declining his own election in that 
example.  That's a large bribe, presumably.

Since withdrawal decisions would be scrutinized by the media, 
they'd better appear clean, else political careers would be 
ended and winners recalled by petition.  

And though Davison may not get it, others will understand that 
there's no fundamental reason to be concerned if one of the 
sincere top cycle is elected.

It also makes sense, if it's reasonable to suppose that 2/3 of 
the top cycle might be corrupt, that sometimes 1/3 of the top 
cycle might be corrupt.  Compare JITW with nonJITW when 1/3 is 
corrupt:  With nonJITW, the corrupt one will win 1/3 of the 
time, wherease JITW would allow the two who aren't corrupt 
to defeat the one who is corrupt.

Given a JITW method, half of the opportunities for post-
election bribery would likely be bribes to NOT withdraw.  
That's something which a corrupt candidate could get for 
free in a nonJITW method, and even when the one not 
withdrawing (because he can't in a nonJITW method) is 
not corrupt.

Presumably, candidates would be asked to make pre-election 
promises regarding withdrawal.  If voters aren't satisfied, 
they can downrank candidates whose answers are troublesome.  

Bart Ingles wrote that he couldn't go along with JITW, but 
declined to state a reason why.  Since he hasn't gone along 
yet with any preference order method, there's nothing there 
requiring a reply.

Bart also suggested a vague alternative which, if it worked as 
hoped, I would agree is better than JITW.  Bart suggested we 
try to find some formal procedure in which candidates could 
voluntarily publish pre-election withdrawal contingency plans, 
then the tallying algorithm would consider those contingency 
plans and automatically withdraw candidates when appropriate.  
I briefly considered this approach last year, and my tentative 
conclusion was that this is not something which is easy to 
make work as desired.  But I would like for my tentative 
conclusion to be disproved; if someone cares to suggest a 
rigorously-designed contingency plan syntax and a robust 
algorithm for processing the contingency plans, I'd welcome 
the efforts.

Markus hasn't provided any persuasive reason not to use JITW.  
He made a vague comment that it would be a catastrophe.  
But he hasn't explained why JITW//IRV would be worse than IRV; 
nor has he explained why JITW//topcycle would be worse than 
topcycle, for some good topcycle method.  He's devoted some 
time to undermining my overstated guarantee regarding regrets, 
for which I thank him, but I'd prefer hearing clear arguments 
for or against using JITW.

One example Markus gave was that two members of the top cycle 
might agree to share power: one might appoint the other his 
"vice" and then resign after half a term.  So what? -- that 
outcome is as good as any since both are in the top cycle.
It sounds like a government of broad consensus, similar to 
what happened in Israel during the 1980s when Labor and Likud 
agreed to rotate the PM office.

In a semi-private message Markus wrote that a downside of JITW 
is that it would encourage candidates of small organizations 
to run because their decisions on withdrawal could be 
decisive.  But that's only true for JITW//Plurality; if a 
candidate isn't popular enough to avoid being eliminated & 
ignored by the basic method then his withdrawal is irrelevant. 
Given JITW//topcyclemethod, a candidate not in the top cycle 
is irrelevant and wouldn't be especially encouraged to run.  
Given JITW//IRV, a candidate who will be eliminated by IRV 
anyway wouldn't be encouraged to run.

Given any top cycle method, small organizations will be 
encouraged to run candidates if they believe their candidates 
can reach the top cycle:
    49: ABC
     2: B      <--  the candidate of a small organization?
    49: CBA
I don't think this is a problem, and I don't think Markus does 
either since he advocates top cycle methods.

Markus also wrote that he wants the voters to have the last 
word, and JITW would interfere with that.  But by the same 
reasoning, Markus should object to all parliamentary systems 
where the PM & cabinet & control of the legislative agenda are 
selected by the legislature instead of directly by the voters. 
In most "democratic" nations, the PM is selected by the 
legislature in a post-election process: the leaders of the 
many elected parties negotiate in a smoke-filled backroom, 
not limited in any way by the voters' preferences.  (I wonder 
if Davison thinks there's little room for bribery there.)

Technically, JITW doesn't take the last word away from the 
voters.  Given a method like JITW//Schulze, the Schulze tally 
is performed *after* the withdrawals.  (The JITW 'filter' 
selects all alternatives which didn't withdraw by the 
withdrawal deadline.)  So the question is under what 
circumstances would voters would change their preferences 
after the withdrawal deadline, because of withdrawal 
decisions they didn't like.

* *

I recently wrote some software to test 3-alternative scenarios 
for various numbers of voters to find all scenarios where 
reversal of ABC to ACB may defeat "condorcet winner" B, 
electing A.  For simplicity I assumed voters' sincere 
preferences are all strict (no pairwise indifference), since 
this speeds up the program execution and made it easier to 
write.  The software also ignores scenarios where reversal 
causes pairwise ties, since with large numbers of voters 
pairties will be very rare and I didn't want the output to 
depend on my choice of tie-breakers.

The software generated a database of scenarios and calculated 
a number of stats for each method, plus summary stats.  One of 
the stats is related to JITW.  I posited that if more than 60% 
of the voters who prefer C the most also prefer B more than A, 
then C would withdraw and B would not, and the reversal tactic 
would be foiled.

Result: Given Condorcet(VotesAgainst) or Schulze's Method, 
in about 75% of the scenarios where reversal can succeed, 
more than 60% of the C voters prefer B to A, suggesting 
that C would withdraw to defend sincere winner B.

Another interesting result is that in many of the scenarios 
where 60% or fewer of the C voters prefer B more than A, A has 
a better sincere Borda score than B.   When A's sincere Borda 
score is better than B's, I'm not particularly troubled by 
A's election.

I also coded the Copeland//Plurality method, which satisfies 
the top cycle criterion, and found that *in nearly every 
scenario* where reversal may succeed, more than 60% of 
the C voters prefer B more than A.

I'm posting a summary of the software output in a separate 
message.


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