[EM] Spoiler Effect on Wikipedia

Steve Eppley seppley at alumni.caltech.edu
Thu Nov 11 10:42:58 PST 2004


Eric G wrote:
> Unless I am mistaken, Approval Voting does satisfy IIA and 
> I find AV to be a reasonable system. :-)
> This nuance is missing on the page 
> (http://en.wikipedia.org/wiki/Spoiler_effect) as well 
> when it is stated:
>  A voting system which satisfies the independence of irrelevant
>  alternatives criterion is immune to the spoiler effect, 
>  but Arrow's impossibility theorem shows that complete
>  satisfaction of this property is incompatible with other
>  desirable properties of an electoral system.
> Arrow's impossibility theorem only applies to ranked ballot 
> voting methods and AV is not a ranked ballot method.

I prefer more general wordings of Arrow's theorem that 
apply to all voting methods.  The one in my web pages, 
for instance.

Approval fails a "universal domain" axiom, which requires 
the social ordering function or social choice function 
accept from each voter any possible ordering of the 
alternatives.  Some people consider universal domain 
to be a desirable property.  The voters' preferences
might not be dichotomous, for instance.  But this is 
not why I expect Approval will be disappointing. 
(I've given my reasons in the past, and don't feel 
like repeating them here, sorry.)

There's a paragraph about Approval in my discussion of 
universal domain in my web page about Arrow's theorem.
I'll copy and paste it here:

"On the other hand, we are not really limited to Arrow's 
framework, which was designed merely to try to aggregate 
voters' (sincere) preferences.  Although it is reasonable 
to require the voting method to work for any collection of 
preferences the voters may have, it does not necessarily 
follow that no constraints should be placed on the 
expressions voters may make when voting.  For instance, 
the so-called Approval voting method constrains each 
voter to partitioning the alternatives into two subsets, 
which is equivalent to a non-strict ordering that has at 
most two "indifference classes."  It is not a priori 
obvious that the use of voting methods such as Approval, 
which constrain the voters from completely expressing 
their preference orderings, are worse for society, so 
the universal domain criterion should be considered 
controversial until other arguments not explored by 
Arrow are examined (assuming those arguments support 
the conclusion that it is better not to constrain the 
voters from expressing orderings).  In other words, 
other criteria for comparing voting methods, in addition 
to Arrow's criteria, need to be evaluated. (My own 
conclusion is that there are solid reasons why it is 
better not to constrain the voters' expressions, but 
that is beyond the scope of this document.)"


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