[EM] Correction. Big CS fault?
Craig Carey
research at ijs.co.nz
Thu Dec 19 03:20:44 PST 2002
The geometry is not obviously Euclidean since there might not ever be a
formula that calculates the Euclidean distance (the square root of the
sum of the squares of differences in the weights, over all kinds of
papers). Also rules that use normalised weights seem to be less likely.
Suppose there is a triangle defining barycentric coordinates. I.e.
the 3 vertices are at: (x,y,z) = (0,0,1),(0,1,0),(1,0,0).
A circle in that barycentric space can be plotted (e.g. inside of the
triangle).
Then undo the normalising (i.e. multiplying by 1/(x+y+z)) and convert that
to an absolute 3-D space [measuring the counts of 3 ballot papers].
Then a (2-lobed) cone results. The original circle is in the 1 = x+y+z
plane.
This message I reply to is unclear. It has trashy jargon in it by the
looks of it.
[1]
F.S: "favorite"
Readers: maybe that means the 1st preference. Also maybe it is a code
word introducing a '1 winner only' restriction. That has certainly been
the case in other messages to this mailing list.
[2]
F.S. .,,
Others:
How is it possible to take it for granted that voters would make
a particular marking on their ballot papers. If Mr Simmons had of been
thinking of Euclidean geometry, then the fact is that an election is a
point of 0 dimensions having a property of its winners. Surely that is
better than saying that a property of each possible set of winners is
the n-D shape/polytope defining where those candidates win.
Where is the equation that processes the "favorite". An what is the
relationship between the "favorites" and the point. ...
[3]
F.s
At 02\12\18 15:41 -0800 Wednesday, Forest Simmons wrote:
>I took it for granted that "favorite" would also be among the approved on
>Majority Choice ballots, and that favorites would be determined from the
>rankings or ratings in the case of CR or ranked ballots.
>
>But I still think that CS as I proposed it suffers from a fault. If the
>race is perceived as being between candidate A and B, and the race is
"perceived by what" ?. Are you designing axiom/rules ?. The message does
not say that.
>close, it would be tempting to list A as favorite and vote just like
>another member of A's camp in order to add zero to the average distance
>from A, thereby giving A the best chance of winning.
>
>Of course, if your favorite and B were on direct opposite sides of A, then
Normally the space is the space of the weight of each _kind_ of paper.
Favorite maybe means "first" preference (me and Ossipoff are not made to be
relevant).
There is no need to use the word "your".
>moving closer to A would remove precisely as much from B's total as it
>would from A's total, so there would be no advantage to abandoning
>favorite.
>
The paragraph seems to lack a good meaning. If Mr Forest Simmons used the
more discplined notation of writing "1.(B)" to represent the paper of
weight 1 that has only a single preference naming candidate B, and "B"
to represent the candidate B (or the symbol B representing the candidate
of that symbol), then it would be harder to produce mistakes like the
paragraph that Mr Simmons wrote.
Also Mr Forest Simmons could, if he wants, distinguish between "(B)" and
"1.(B)" (alternatives for the latter are "1(B)", and maybe "1:(B)".
>Perhaps the best strategy would be to vote at the foot of the
>perpendicular from favorite's position to the line determined by A and B.
>
Are you giving advice to weighted lists of symbols ?.
The message is not only 80% full of mistakes offering readers an
enjoyable chance to delete and reconstruct Mr Forest Simmons' original
thinking.
>[How to accomplish that is another question.]
>
Why not rewrite this message and use better notation the distinguishes
between a 'paper' (list or weighted list) with 1 preference, and the
candidate named by that paper.
It plain for computer scientists: record type contains a real
number and an array of integers, and similarly it is no simple for
mathematicians. However of all that Forest is borrowing from the
thinking of social decision theorists that aspire to getting at least
one word starting with "Arrow" into their published documents.
>In that case the Euclidean distance would make the most sense.
>
>
>I'll continue in another posting.
>
What happened to the usual theme of not having a definition but
implying it existing since incorrectly saying it was used ?. That
used to be a circumstance in which MIKE used the word favorite.
Just adding padding ...?
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