[EM] Re: Finding the probable best candidate?

[Adam Tarr]

Demorep wrote:

>Head to Head (Condorcet) Table
>
>BR Browne BH Bush BN Buchanan G Gore N Nader
>
>        BR     BH    BN     G     N
>
>BR     xx     62    70     52    49
>BH     38     xx    98     49    49
>BN     30      2    xx     49    49
>G      48     51    51     xx    52
>N      51     51    51     48    xx

At last, someone has displayed this voting set in an fashion that doesn't 
make me go blind.  So... Gore, Nader, and Browne are the members of the 
Smith set.  There is a circular tie between them.  Gore beats Nader 52-48, 
Nader beats Browne 51-49, and Browne beats Gore 52-48.

Since the ballots are all fully expressed, Ranked Pairs and Schwartz 
Sequential Dropping will have the same effect; dropping the Nader-Browne 
victory.  This gives the election to Browne.

If I understand Borda-seeded bubble sort right, it too will have the same 
outcome.  The Borda rankings (ignoring those outside the smith set) are
1) Browne,
2) Gore,
3) Nader.

So Nader fails to advance on his turn, and Gore fails to advance on his 
turn.  Browne then is left in first.

If, on the other hand, say the cyclic ties went the same way, but due to 
Nader running a few clone candidates, the initial order was
1) Nader
2) Browne
3) Gore,

Then Nader wins.  Basically, whoever starts in first place in the cyclic 
tie wins, since whoever makes it up to challenge them must be the candidate 
that loses to them.  So insofar as Borda seeded bubble sort uses Borda 
count to decide things, it has the same strategic problems as Borda.

-Adam