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 r...@audioimagination.com
"Imagination is more important than knowledge."
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