# Circular Tie solution

donald at mich.com donald at mich.com
Fri Nov 8 06:02:32 PST 1996

```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.

I have a second circular tie solution.

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.

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!

Donald

```