[Election-Methods] Which monotonicity?

[Chris Benham]

Stéphane Rouillon wrote:

>I am fed up a bit with that discussion about non-monotonicity because it 
>depends how
>monotonicity is defined.  IRV is monotonic when you consider adding or 
>retrieving
>ballots with you preffered candidate as first choice. IRV is non-monotonic 
>when
>you consider highering or lowering the positions of your preferred candidate 
>on several ballots...
>
>Maybe some concision and precision in the definitions would help.
>Could we use 2 different names for monotonicities please?
>Or maybe they exist and I don't know these definitions...
>
>S. Rouillon
>

In this 1996 paper  Douglas Woodall defines and discusses some different 
versions of  "monotonicity":

http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf

http://wiki.electorama.com/wiki/Monotonicity_criterion

http://wiki.electorama.com/wiki/Mono-add-top_criterion

Two that Woodall only mentions in that paper,  "Mono-append" and  
"Mono-add-plump"  are very very
weak (meaning very easy to meet) and not doing so is (in my book) very 
very silly.

"Mono-add-plump" says that adding ballots that plump for X (i.e. 
"bullet-votes" for X) should never reduce
X's chance of winning.

"Mono-append" says  that if some ballots that didn't rank X (above 
equal-bottom) are changed so that now
X is ranked immediately below the candidates that previously were the 
only ones ranked (above equal-bottom),
then X's chance of winning must not be reduced.

(These definitions are my paraphrasing)

Chris Benham


>
>  
>
>>From: Jonathan Lundell <jlundell at pobox.com>
>>To: Steve Eppley <SEppley at alumni.caltech.edu>
>>CC: election-methods at electorama.com
>>Subject: Re: [Election-Methods] Why monotonicity?
>>Date: Tue, 15 Jan 2008 08:38:36 -0800
>>
>>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.
>>----
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>>    
>>
>
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