# Circular Tie solution

Mike Ossipoff dfb at bbs.cruzio.com
Fri Nov 8 09:44:03 PST 1996

```donald at mich.com writes:
>
> Dear List,
>
> Steve wrote:
> >Donald suggested a couple [of] improvements to Condorcet.
> >
> >Ha ha, I get it, even without a :-) hint.
> >
> >---Steve     (Steve Eppley    seppley at alumni.caltech.edu)
>
> Donald: I was wondering if I could slip that pass the pairwise guys - you
> are wise indeed.

Sorry I missed your joke. When I noticed that you didn't give any
compact definition of the method, at least not an intelligible one,

Speaking of jokes, hasn't your participation in this list been
pretty much in the nature of a joke from the start? You admit that
you spout off on the subject without having read the previous letters
on the subject.

>
>
> I have a second circular tie solution.

Is it a joke too? Has it occurred to you that maybe you're
wasting our time?

>
> The logic of this solution is as follows:
> If the pairing of the candidates is valid - "a good and proper thing to do".
> Then it follows that adding all three pairings together should also be
> valid - mathematically correct and a good and proper thing to do.

Excuse me for replying serioiusly if this is just another joke, but
there's no reason to believe that it would be meaningful to add all
three pairings together, whatever that means. At least not meaningful
in terms of the goals that lead to the pariwise methods, & Condorcet
in particular.

It's been pointed out that adding up votes-for in each of an alternative's
pairings is equivalent to the Borda point system, a method notorious for
its violation of majority rule & its strategy problems.

>
> So - going back to DEMOREP1's example:
>
>                              H and G        H and S        G and S
> DEMOREP1's                   Pairing        Pairing        Pairing
> Example
> 35 HG                        35H            35H            35G
> 33 GS                            33G            33S        33G
> 32 SH                        32H                32S            32S
> H beats G, 67 to 33         --------        -------        -------
> G beats S, 68 to 32          67H 33G        35H 65S        68G 32S
> S beats H, 65 to 35
> Circular Tie---  H>G>S>H
>
> Donald: When we add together the results of these three pairings we get the
> following:
>
>                             67 H      33 G
>                             35 H                65 S
>                                       68 G      32 S
>                            -----     -----     -----
>                            102 H     101 G      97 S
>
> Again we have a winner - no circular tie. Now of course - in another
> example it may be possible to have a tie between the top two - a tie that
> can be solved by using Instant-Run-off - HA HA!

Ha Ha. How about taking it somewhere else?

>
> Donald
>
>
> .-
>

--

```