# [EM] Sincere Condorcet Cycles

robert bristow-johnson rbj at audioimagination.com
Sun Dec 13 21:30:16 PST 2009

```On Dec 14, 2009, at 12:06 AM, Dan Bishop wrote:

> robert bristow-johnson wrote:
>>
>> On Dec 13, 2009, at 7:53 PM, fsimmons at pcc.edu wrote:
>>
>>>  Here's a natural scenario that yields an exact Condorcet Tie:
>>>
>>> A together with 39 supporters at the point (0,2)
>>> B together with 19 supporters at (0,0)
>>> C together with 19 supporters at (1,0)
>>> D together with 19 supporters at (4,2)
>>>
>>> D is a Condorcet loser.
>>> A beats B beats C beats A, 60 to 40 in every case.
>>
>>
>> i wouldn't mind if someone could decode or translate the above.
>> what does "at the point (x,y)" mean in the present context?
>>
>> much appreciated.
> They're coordinates in a 2-dimensional political spectrum.
> Assuming Euclidean distances are used, the ballots are:
>
> 40: A>B>C>D
> 20: B>C>A>D
> 20: C>B>A>D
> 20: D>C>A>B

thanks.  where i am still lacking is understanding how the latter is
derived from the former.  is there some 2-dimensional distribution of
voters in this plane and the voter's ballot is evaluated and
preference is a strictly decreasing function of the distance?  or are
they all at only those 4 points?  i don't consider that natural.  i'm
pretty much what South Park typecasts as "Aging Hippie Liberal
Douche" but you might find me an issue where i just do not identify
with the Democrats (or in Vermont, the Progs).  not every voter who
is primarily for A is gonna consider B to be better than satan.

i think maybe i now understand how the latter is derived from the
former.  if i do, then i don't consider the scenario to be
particularly natural.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."

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