[EM] Anyone got a good analysis on limitations of approval and range voting? (long)

[Juho]

In large elections with evenly spread voters and candidates and no  
strategies the distribution of Approval votes may indeed be such that  
the best candidate regularly wins. The situation may however be also  
different. I  gave one simple example where the left wing had two  
candidates and the right wing had only one. The distribution of votes  
may not bring fair results in this type of set-up.

The assumption was that the right wing voters would predominantly  
approve only their own candidate while many left wing voters would be  
tempted to indicate which one of the left wing candidates they prefer  
over the other (despite of clearly preferring both left wing  
candidates over the right wing candidate). The end result could  
therefore be biased. The right wing candidate might easily win even if  
right wing would have considerably smaller than 50% support.

With small number of candidates and with a candidate set-up that is  
not symmetric or well balanced Approval may well produce biased  
results. Methods that are capable of providing richer information  
(ranked methods) are likely to provide more balanced input data (and  
results).

Juho


On Nov 12, 2009, at 2:28 AM, robert bristow-johnson wrote:

> On Nov 10, 2009, at 7:40 AM, Matthew Welland wrote:

>> It is the aggregate of
>> thousands or millions of votes that will make or break A vs. B. How  
>> many
>> feel so strongly against A that they cannot vote for him or her?
>>
>> The binary nature of approval is washed out by large numbers just  
>> as a class
>> D amplifier can directly produce smooth analog waveforms out of a  
>> pure 1 or 0
>> signal.
>
> the mathematical function that does that is the low-pass filter on  
> the output.  it's sorta the same idea that these 1-bit A/D (a.k.a.  
> "sigma-delta") converters use.  if we were voting with a range  
> ballot, and our continuous range value gets a zero-mean uniform  
> p.d.f. random "dither" signal added to it (or, to use your PWM  
> example, a zero-mean number drawn sequentially, in chronological  
> order of the vote submission) and that gets quantized to a yes/no  
> Approval vote (i s'pose if the threshold is set to 50%), then you  
> would have a comparable situation.
>
> i just dunno if i like the idea of a zero-mean (and even symmetrical  
> p.d.f.) random variable actually going into a governmental  
> election.  how well i approve or disapprove of a particular  
> candidate that i am not actively supporting is a function of how i'm  
> feeling on Election Day.  but it's less likely how i rank that  
> candidate w.r.t. the other candidates would change.  like grading  
> papers, sometimes to come up with a numerical score, we get out our  
> dartboard and see how good our toss is.  but students might like a  
> more deterministic method.
>
> for governmental elections, i only support a system that is fully  
> deterministic (and repeatable) except, i s'pose, if there is a dead  
> heat, then i s'pose, some kind of drawing of lots would be  
> necessary.  it should require enough information from voters that  
> the system knows how any voter would choose between any subset of  
> candidates (the ranked ballot does that, but the approval ballot  
> does not).  and it shouldn't force voters to bring their dartboard  
> (or dice or spinner, etc) to the polls to come up with a numerical  
> approval rating for each candidate, because of GIGO.
>
> the other principle that is important is that of anonymity of vote.   
> it shouldn't matter if you really, really, really like your  
> candidate and i only tepidly support his/her opponent.  my vote for  
> the opponent should count just as much as your more enthusiastic  
> vote for your candidate.  there should be nothing that tips the  
> scale in favor of your candidate based on how enthusiastically she  
> is supported, only by the numbers of voters that supports her.  our  
> votes should have equal weight.
>
> --
>
> r b-j                  rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
>
>
>
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