Arrow/IA/IIAC

[David Catchpole]

On Sat, 11 Mar 2000, David Catchpole wrote:

> On Sat, 11 Mar 2000 DEMOREP1 at aol.com wrote:
> 
> > Which is the highest head to head majority (and thus the most likely correct) 
> > ? 65 BC (with C being the most likely clone)    Duh ?
> 
> A voting paradox will still exist in several cases in which, at least, the
> addition of a close clone will punish its voters. This was the first
> result I got when I started playing around about 6 months ago with "no
> splitting" rules, and I'll try to remember a specific example.

'Ere dooz- the simple "confused and irrational voters" system-

2	3	4
A	B	C
B	C	A
C	A	B

Now, let's expect that when a new candidate enters the race, it should
benefit or at least have no effect on the people who preferred the new
candidate to both the "old" and the "new" winner- that is, it genuinely
benefited these voters to support this new option. Let's now demonstrate
that this expectation can't be satisfied...

Say only A and B run. A wins. Now, C runs. If B wins in the A,B,C case it
punishes C voters.

Say only A and C run. C wins. Now, B runs. If A wins in the A,B,C case it
punishes B voters.

Say only B and C run. B wins. Now, A runs. If C wins in the A,B,C case it
punishes A voters.

In other words, any result for the A,B,C case will punish voters for a
"minor" candidate. It was always my opinion that Demorep would be most
offended by this occuring.

> Almost all voting paradoxes, including that at the centre of Arrow's
> theorem, are generated by the absence in some cases of a Condorcet
> winner. If we could exclude or ignore all cases in which this absence
> occured, life would be hunky dory, but unfortunately this is not the case.
> 
> --------------------------------------------------------------------
> Atheists aren't vagrants- but we have no invisible means of support.
> 
> 

--------------------------------------------------------------------
Atheists aren't vagrants- but we have no invisible means of support.