[Election-Methods] Why monotonicity?

[Jonathan Lundell]

On Jan 15, 2008, at 8:22 AM, Steve Eppley wrote:

> The strategy of raising a candidate in order to defeat it may
> legitimately be counted as one more strategy in the voter's toolbox of
> strategies, but I think the (narrow) question here is whether the  
> number
> of manipulable scenarios is greater given non-monotonic methods, given
> the same set of candidates and same voters' preferences.  To my
> knowledge, this has not been demonstrated.
>
> Furthermore, since the assumptions of the same set of candidates and
> same voters' preferences are dubious--candidates may adopt different
> positions on the issues, and make different decisions about whether to
> run, given a different voting method--monotonicity may be unimportant
> even if it does reduce the number of manipulable scenarios.
>
> I think all we can say for sure about the desirability of monotonicity
> is that, all else being equal, it's better to be monotonic.

I'm reminded of Douglas Woodall's argument that STV's monotonicity  
failures occur in scenarios where it's not obvious to begin with which  
candidate(s) "ought" to be elected.

http://www.votingmatters.org.uk/ISSUE4/P5.HTM

> There are certain regions in which it is quite clear who ought to be  
> elected, and in these regions STV elects the candidate that one  
> would expect. But in the middle there is a grey area, where it is  
> not at all clear who ought to be elected, and it is in this grey  
> area that STV behaves in a somewhat haphazard manner; it is really  
> doing no more than making a pseudo-random selection from the  
> appropriate candidates, and it is here that small changes in the  
> profile of ballots can cause perverse changes in the result.
>
> The effect of this is to blur the result of an STV election. Nobody  
> is being wrongly elected, because the problem only arises in the  
> region where one cannot say for certain who ought to be elected  
> anyway. And there is no systematic bias that would, for example,  
> favour one political party rather than another. But the accuracy  
> with which the person or persons elected in an STV election can be  
> said to represent the views of the voters is less precise than it  
> would be if this sort of anomaly did not arise.
>
> The obvious question at this point is whether one can find a system  
> that retains the essential features of STV while avoiding this sort  
> of anomaly. The answer depends on what one regards as the essential  
> features of STV. As we shall see in a later article, it is not  
> possible to avoid this anomaly without sacrificing at least one  
> property that many supporters of STV regard as essential.
>

...by which he means later-no-harm.