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<DIV dir=ltr align=left><SPAN class=632501623-14122005><FONT face=Arial
color=#0000ff size=2>I think the effect of what we said about ties is usually
the same. Critical to any method, though, would be to record an A=B>C as
having C in the third-place spot. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=632501623-14122005><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=632501623-14122005><FONT face=Arial
color=#0000ff size=2>Things get kind of complicated when you get into 1/2 a 1st
place vote and 1/2 a 2nd place vote. A and B both get the same value, but is
that more or less than one of each compared to the other alternatives? When you
assign values to rankings, you're introducing Borda into the collection process.
</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=632501623-14122005><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=632501623-14122005><FONT face=Arial
color=#0000ff size=2>I prefer 1,1,3 to be saved as 1,1,3 for A,B,C. 1.5,1.5,3
could have the collection method impact the results.</FONT></SPAN></DIV><BR>
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<FONT face=Tahoma size=2><B>From:</B> rjbrown@gmail.com
[mailto:rjbrown@gmail.com] <B>On Behalf Of </B>rob brown<BR><B>Sent:</B>
Wednesday, December 14, 2005 5:12 PM<BR><B>To:</B> Paul Kislanko<BR><B>Cc:</B>
honky98@aggienetwork.com; Election Methods Mailing List<BR><B>Subject:</B> Re:
[EM] number of possible ranked ballots given N candidates<BR></FONT><BR></DIV>
<DIV></DIV>On 12/14/05, <B class=gmail_sendername>Paul Kislanko</B> <<A
href="mailto:kislanko@airmail.net">kislanko@airmail.net</A>> wrote:
<DIV><SPAN class=gmail_quote></SPAN>
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<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN>Just a
thought for your endeavor. A way to save "more" information than the
pairwise matrix but less than saving counts of each ballot configuration is
to save an NxN matrix with column headings being count of #1, #2, ... #N
ranks and rows being the Alternatives. Use the rule:</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff
size=2><SPAN></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN>If
equals are found, assign the next alternative rank (r+1) where where r is
the rank the previous alternative listed would've had if there were no
equals. I.e. ranks are assigned 1,1,3 for A=B>C. </SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff
size=2><SPAN></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN>This
takes no more space than the pairwise matrix, but contains much more
information. See <A onclick="return top.js.OpenExtLink(window,event,this)"
href="http://football.kislanko.com/2005/bucklincomps.html"
target=_blank>http://football.kislanko.com/2005/bucklincomps.html
</A> for an example with 119 alternatives and any number of
voters.</SPAN></FONT></DIV>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: rgb(0,0,255) 2px solid; MARGIN-RIGHT: 0px"></BLOCKQUOTE></BLOCKQUOTE></DIV>Our
messages overlapped, each trying to find a way to store more data without
storing all ballots. :) <BR><BR>Your suggestion seems like something you'd
want to store in addtion to the matrix, no? It seems like it would be
hard to perform the sort of calculations that the matrix works well for, i.e.
picking a candidate in a way that doesn't encourage strategic voting and
doesn't punish (or reward) candidates for having other candidates that appeal
to the same constituency. <BR><BR>BTW, if it was me I would handle ties
differently, for two candidates tied for first, I would probably want to store
half a point for first place and half a point for second place for each
candidate. In other words treat 2 A=B>C ballots as being functionally
identical to 1 A>B>C ballot and 1 B>A>C ballot. But that's
just me. <BR><BR>-rob </BLOCKQUOTE></BODY></HTML>