[EM] Ranked Preferences, example calculations

[Chris Benham]

Abd ul-Rahman Lomax wrote:

>At 11:34 PM 10/27/2006, Chris Benham wrote:
>  
>
>>Abd ul-Rahman Lomax wrote:
>>
>>    
>>
>>>That is, healthy group decision process follows certain general 
>>>principles. The Majority Criterion neglects an important part of this.
>>>
>>>      
>>>
>>That is because it is about *elections*, which of course isn't 
>>necessarily the beginning and end of  "healthy group decision process".
>>    
>>
>
>For some reason, Chris continues to insist upon the specious 
>distinction between elections and general decision-making process. 
>The term "election" covers any kind of choice being made; however 
>usage focuses on the selection of one candidate out of a number, for 
>single-winner, or of multiple candidates out of a larger number, for 
>mutiple-winner. And we also assume, generally, for the purposes of 
>this list, that elections are of candidates, and the candidates are 
>people who will hold an office.
>
>But for a group to select candidates or to select a pizza involves, 
>properly, the same considerations. Pizza is almost certain to be less 
>important a choice, but the importance of the choice only should mean 
>that greater care would be taken. Not that a different process is involved.
>  
>
CB: No.I see "group decision making process" as spread out along a 
continuum with "informal consensus"
at one end and civil war or violent "mob rule" at the other. Abd sees 
elections as (in his view undesirably)
substituting for consensus and wants to change them into mechanisms for 
reaching a formal consensus,
whereas I think they should more properly be seen as tough competitions 
that substitute for civil war.

A group of people ordering pizza are presumably a freely associating 
group of friends, so all are
considerate of the other's strong preferences (and "needs") and no-one 
wants to oppress  anyone  or
listen to anyone whingeing while they are trying to enjoy their pizza. 
(And of course if anyone is really unhappy
they can presumably just leave the group and not starve.)So in that case 
of course the group would
probably quickly come to an informal consensus, and if there *was* any 
formal "voting" then I suppose
some variation of  Range or Approval would do and may be best.

But suppose in an experiment to please Abd, the pizza orderers aren't 
friends and maybe even dislike
each other, they are very hungry and there won't be enough pizza to 
satisfy everyone's hunger and the
people are locked in the room with nothing to eat but this pizza they 
are ordering. Then "informal consensus"
will tend to break down and we will have a scenario more appropriate for 
a tough election. Voters might
have incentive to vote for a variety others dislike in the hope they 
will then get a bigger share.

>
>The only substantial argument I see against Range is that the method 
>is allegedly vulnerable to strategic voting. *But what we have now is 
>what Range would look like if everyone votes strategically.*
>
>
>So Range would not make things worth, unless... unless honest people 
>vote intermediate values, and dishonest people vote the extremes, and 
>there are enough of these dishonest people that election results are 
>warped as a result.
>
>However, I have argued that this can only happen when the honest 
>people do not have a strong preference. When they have, and express, 
>a strong preference, and they are in the majority, the dishonest 
>people can try what they may, they can only nudge the results among 
>candidates strongly preferred by the majority.
>  
>
A "strong preference" for *what* exactly?.. that a single candidate be 
elected, that a single candidate
not be elected, that the winner come from a certain set, what?

>Essentially, some writers treat the vulnerability of Range to 
>strategic voting as if it were a proven thing. They simply assume it. 
>It has *not* been proven, far from it. And it seems to me that this 
>is a false charge against Range.
>
>  
>
It would. It is obvious to anyone with a clue that it is.

>E
>  
>
>>>That is, if the majority does not want to please the minority, it 
>>>does not care if they are devastated by the outcome of the 
>>>election, if their attitude is "they should get over it," then they 
>>>can easily get what they want. Just vote it as a strong preference.
>>>
>>>      
>>>
>>The problem with Range is that if  "the majority" are not self-aware 
>>and coordinated, they cannot
>>"easily get what they want".
>>    
>>
>
>On the contrary, the condition being described was that the majority 
>had a strong preference. Under Range, all they need to do is vote 
>that preference as a strong one. What coordination does this take?
>
>  
>
Again "strong preference" for what exactly?  And how strong is "strong"?

>This has been stated so many times by Warren, but obviously it bears 
>repeating. The best vote in Range is a sincere one. Sure, partisans 
>may distort their votes, turning them into black and white. But by so 
>doing they are essentially eliminating their own true preference 
>strengths from the election. They are harming themselves, not the 
>society, except to the extent that the society is harmed when 
>individuals are not satisfied. They are risking their own 
>dissatisfaction, if it turns out that, by voting black and white, 
>they effectively abstained from voting in the top two pair-off.
>
>  
>
I  suppose it would be too much to expect any examples or evidence in 
support of this
fantastic nonsense?

Range has no real "majority-rule" related guarantees, except a very 
unimpressive weakened
version of  Minimal Defense that means that for a majority to block the 
election of X they
must both give X a minimum rating and some other candidate a maximum rating.

But since Range is a deterministic method, the lack of guarantees for 
the majority necessarily
make it vulnerable to strategy.

25001: A99>B98>C0
25000: B99>A98>C0
49999: C99>A0=B0

Here a majority express the strongest possible preference that C not win 
without falsifying their
sincere rankings, and yet C wins.  This demonstrates (proves) that Range 
fails Majority Loser,
Condorcet, Majority for Solid Coalitions and (regular) Minimal Defense.

These failures make Range in this case vulnerable to Compromise 
strategy. If  the 2500 B99>
A98 voters change to B99=A99, the winner changes from C to A (who they 
vastly prefer).

25001: A99>B98>C0
25000: B99=A99>C0  (sincere is B>A>>C)
49999: C99>A0=B0

This Abd, is *proof* that Range is vulnerable to the 
Compromise(compression) strategy.
"Compression" refers to the fact that they only have to "compress" their 
B>A preference to B=A.
Because Range/Approval meet the Favourite Betrayal Criterion  and 
Sincere Favourite (FBC/SF)
they don't have to actually reverse from B>A to A>B.

36: A99>B98>C0
18: B99>B98>C0 
46: C99>A0=B0

This time the AB have a comfortable enough majority to win without 
insincere equal-ranking, and
A (the Condorcet and IRV winner) wins.  But Range (like Approval) is 
vulnerable to a form of
Burial with a nasty defection incentive.

36: A99>B98>C0
18: B99>B0=C0   (sincere is B>A>>C)
46: C99>A0=B0

The 18 B voters have "defected" from the AB coalition by insincerely 
changing from B99>A98
to B99>B0=C0, and Range rewards their dishonesty (and disloyalty) by 
electing B.

(Note to Abd: this *proves* that Range is vulnerable to the Burial strategy)

Of course if  the A supporters also defected then C would win, and that 
would be an example
of a "majority" (a sincere majority solid coalition) not being 
"coordinated".

The type of election scenario illustrated by these examples, polarised 
with one united faction
confronting two sub-factions, is much better handled by IRV than by 
Range or Approval.

>Majority Rule. What a concept!
>
Yes. Please make up your mind whether you are in favour of it or not.

>>>And thus, respecting the majority principle, I've suggested that 
>>>the election of a Range winner over a Preference winner should be 
>>>ratified by the electorate, either by a pure ratification vote or by a runoff.
>>>      
>>>
>>So what exact method do you propose be used to determine "the 
>>preference winner"?
>>    
>>
>
>The simplest would be a Majority winner. It might be the Plurality 
>winner. Or the Condorcet winner. However, a Condorcet winner who has 
>only a small percentage of the first-preference vote is probably not 
>worth electing, if there is a clear Range winner; likewise a 
>Plurality winner. I'm not sure exactly what winner would best be 
>chosen, it would be worth considering. The Range ballots would be 
>analyzed by converting them to ranked ballots, which is trivial 
>(equal ranking allowed).
>
>I'm inclined that it be a Majority winner. Remember, the objection 
>was that somehow choosing the Range winner would be a violation of 
>majority rule. Well, this would guarantee that majority rule would 
>not be violated.
>
"Majority winner" (presumably referring to a single candidate who is the 
favourite of more than
half the voters) and "Plurality winner" both have a split-vote problem 
(failing Clone-Winner) and
of course there isn't always a Condorcet of "Majority" winner.

>(I oppose public campaign financing, it is the wrong approach, but it 
>*does* exist and is going to be a problem in election reform.)
>  
>
It works quite ok in Australia. What do you suggest to address the 
unfair advantage of  Big Money
in election campaigns?


Chris  Benham










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