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<DIV><FONT face=Arial size=2>Isn't there really anyone interrested in this topic
? </FONT></DIV>
<DIV><FONT face=Arial size=2>Or am I just much too confusing in my
explanations ???</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I'd like to get feedback on this topic,
please...</FONT></DIV>
<DIV><FONT face=Arial size=2>It's about normalising the enthropy (amount of
information) </FONT></DIV>
<DIV><FONT face=Arial size=2>contained in of an "approval like"
vote.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Philippe Errembault</FONT></DIV>
<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV><FONT face=Arial size=2></FONT><FONT face=Arial size=2></FONT><FONT
face=Arial size=2></FONT><BR></DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>Hi all,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Sorry about not reading ALL your mails. It
could happen that the question I'm going to ask has already be
processed...</FONT></DIV>
<DIV><FONT face=Arial size=2>... But since english is not my mother tongue and
since you write much ;-) and since there is only 24h in a day and since blah
blah blah ;-) ...</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>So...</FONT></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>I'd like to have your opinion about an idea concerning <FONT
face=Arial size=2>the impact of voting for multiple people :</FONT></DIV>
<DIV> </DIV>
<DIV>In any approval-like system, where you can give your voice to more than
one candidate, you have a problem since giving voices to multiple
candidate raises the weight of vote. Especially if a group of voters give
their voice to the same specific group of candidates, the will drasticly raise
the chances of all their vote to match with other voters who didn't arrange
with them.</DIV>
<DIV> </DIV>
<DIV>So, why not evaluate the amount of information (let's call it
[I]) contained in a vote, and weight this vote by 1/[I] !?</DIV>
<DIV> </DIV>
<DIV>first idea : let's give the value 1 to each approval to a candidate and 0
for others. the vote will then be a set of 1 and zero, for wich we can
compute the average, variance and standart deviation. Let's use standard
deviation for [I] and each vote by 1/[I].</DIV>
<DIV> </DIV>
<DIV>this reduces impact of explicit arrangement, but not for implicit
arrangements : let's call implicit arrangement, the fact that a well
known has more chances than others to accumulate random votes,
so people voting for them will have more chances to match other voters.</DIV>
<DIV> </DIV>
<DIV>second idea : instead of using each approval and disapproval, let's count
them as many times as the count of votes received by the candidate to compute
the standard deviation.</DIV>
<DIV> </DIV>
<DIV>I have attached a small excel simulation but I'm not sure it
will be accepted on the mailing list.</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>procedure : </DIV>
<DIV> </DIV>
<DIV>for each voter [i], for each candidate [j], the voter chooses [Vij] to
approve ([Vij] = 1) or not ([Vij] = 0) the candidate.</DIV>
<DIV>then, for one candidate, let's call </DIV>
<DIV> [Sj], the sum of [Vij] for
all voters [i].</DIV>
<DIV>and [S] is the sum of [Sj] for all candidates [j].</DIV>
<DIV> </DIV>
<DIV>then, for one voter [i], let's call </DIV>
<DIV> [AVGi] the average of [Vij], each [Vij] counting [Sj]
times. ( [AVGi] = SUM( [Sj]*[Vij] ) / [S] )</DIV>
<DIV> [VARi] the variance of [Vij], each [Vij] counting [Sj]
times. ( [VARi] = SUM( [Sj] * ([Vij]-[AVGi])^2 ) / [S] )</DIV>
<DIV>
( or [VARi] = SUM( [Sj]*[Vij]^2 ) / [S] -
[AVGi]^2 )</DIV>
<DIV>(where ^2 means squared)</DIV>
<DIV> [SDVi] the standard deviation of [Vij]. ([SDVi] =
Square Root([VARi]);</DIV>
<DIV> </DIV>
<DIV>so each votes are weighted with 1/[SDVi] and each candidate receives
SUM([Vij]/[SDVi])</DIV>
<DIV> </DIV>
<DIV> </DIV></FONT></DIV>
<P>
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