[Election-Methods] Why monotonicity? (was: Smith +mono-add-top?)

[Juho]

Good discussion. In general I think a strict criterion fulfillment  
based evaluation of the election methods is not sufficient.  
Monotonicity can be seen as a property that is always positive but  
that need not necessarily be always met. It is enough if in the given  
environment voters need not worry about their vote potentially being  
non-monotonic (so much that they should consider voting another way).

Also many other criteria have similar properties. There are actually  
very few that would be fully strict. Condorcet criterion seems to be  
one that is widely accepted and recommended for competitive  
compromise seeking elections (excluding Range supporters ;-) (IRV  
supporters are maybe not seeking for a compromise candidate).

I'm inclined towards evaluating methods based on the worst real life  
examples that can be generated (for the environment in question). It  
would be good to complement also listed failures of different formal  
criteria with examples on what will happen when they are not met.  
Practical examples are good in checking that the assumed threats/ 
problems are also practical in the sense that they can be implemented/ 
have influence in real life (with incomplete information and  
incomplete control of the voters).

Juho


On Jan 2, 2008, at 17:58 , James Gilmour wrote:

> Jobst had written:
>>> Also, it seems difficult to sell a method when you must admit that
>>> advancing an option X may actually reduce X's winning probability...
>>>
> Steve replied:
>> That doesn't seem to be a problem for the Instant Runoff  
>> campaign.  ;-)
>> Do you recall an example where it was difficult to sell a method  
>> due to
>> its non-monotonicity?
>
> This should be no surprise because, at least in public elections  
> with hundreds, thousands or ten-of-thousands of voters in each
> electoral district, non-monotonicity cannot be exploited either by  
> the candidates or by the voters.  It could be very different in
> successive elections by IRV or STV-PR where the whole electorate  
> was a small committee of, say, ten members  -  then it MIGHT be
> possible for some voters to change their preference patterns to  
> exploit the non-monotonicity to the benefit of their preferred
> candidates.   But monotonicity is a completely irrelevant criterion  
> so far as public elections are concerned.
>
> James Gilmour
>
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