Ideal (?) Gaussian Consensus
Saari at aol.com
Saari at aol.com
Mon Apr 14 16:14:41 PDT 1997
>Mike Saari wrote:
>>For a simple Gaussian distribution, clearly the "best" result is at the
>>middle of the central peak, i.e. at the 50-percentile point. Surely we can
>>all agree on this, right?
>Donald writes: Wrong! Sorry Mike - but I do not agree. I do not accept this
>habit that people have of placing candidates and people on a line - left to
>right - and then saying that the central point is the consensus.
I agree, but you've missed the point of my argument. I agree with you that,
in many or most cases, it is invalid to assume that candidates can be
represented as a single variable. My point was not to try to lump all of
reality into this very simple model - this is clearly unwarranted.
The point I am trying to make is: IF a situation can be fairly described as
a standard Gaussian distribution on a single variable only, THEN it is
reasonable that the voting paradigm should select the most central candidate.
Never mind that reality is usually more complex. I'm just saying that, for
a given (very simple) situation, we should expect our voting system to
produce the right result.
It is like we are designing a calculator capable of solving a variety of
higher math functions. The "Gaussian" test is like saying "Let's also make
sure that our calculator can properly add 2+2 and get the right result."
Naturally, this does not guarantee that it produces the right result for
more complex calculations. However, if it does NOT produce the right answer
for 2+2 we have reason to reject it as flawed.
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