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

[robert bristow-johnson]

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

> Also, again, your single vote is irrelevant.

except in a close election.

> 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."