[EM] Majority Criterion, hidden contradictions

[Chris Benham]

Abd ul-Rahman Lomax wrote:

>As written, AV satisfies the MC, and the arguments I see 
>on this, so far, do not really address the issue.
>
What issue? Since you don't support the "MC", why do you even care if it 
does
or not?

>Show me a proof 
>that AV does not satisfy the MC, but Plurality does.
>
>To do so, you must define "strictly prefer."
>
"Strictly prefer" means exclusively prefer. The "Majority Criterion" (I 
don't like this name
because Woodall uses it to refer to Majority for Solid Coalitions. I 
prefer "Majority Favourite"
or "Majority for a single candidate") means that if more than half  the 
voters prefer X to all
other candidates, then X must win".

What Approval in effect does is ask the voter to divide the candidates 
into two sets at his/her
discretion (technically one of these sets may even be empty) and then 
tell us which set s/he prefers
to the other. Only if the voter's preferred set happens to have one 
member can we infer which
candidate that voter prefers to all others.

So really since the method doesn't ask the voter which candidate is 
their exclusive favourite, it
has no way of  "knowing" who is the favourite of the majority is and so 
of course can't and doesn't
 meet Majority Favourite/MC.

Abd isn't the first sophist to try to argue that if a voter puts more 
than one candidate in his/her
preferred set, that must mean that he/she means to rank them all equally 
in first place and so
therefore if a majority don't put X alone in their preferred set X can't 
be the majority favourite.

(But that is like me gluing your legs together and then pretending that 
you only have one leg.)

>These voters, who have elected to use Approval 
>in this way, have abstained from indicating the "strict preference" 
>which is part of the Criterion, and therefore they are not party of 
>the "majority."
>
The criterion doesn't stipulate that the majority have to be willing to 
pay a price or engage in
some perhaps risky strategy to express their strict preference for X 
above all others.

>>It is not accurate or honest to ignore voter preference or treat it as
>>irrelevant when the ballot does not allow it to be expressed!
>>    
>>
>
>Does Plurality allow the expression of preference? How?
>  
>
The only "preference" the criterion is concerned with is the first one, 
and that is the one that FPP
allows voters to express.  Making the comparison with Approval, if the 
voters are constrained to
put a single candidate in their "preferred set", then of course that 
candidate is their clearly voted
strict favourite.


Chris Benham



 







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