Pairwise Rated Benchmarks

[DEMOREP1 at aol.com]

Mr. Ingles wrote in part--

I have been advocating the use of rated sincere-voter scenarios for two
purposes:

1)  To allow setting up hypothetical situations where there is a
reasonable chance of predicting how voters will behave under various
actual methods when tactics are considered, and thus of predicting the
outcome under different methods, without necessarily saying which
outcome is the correct one.

Under Approval voting, especially, it would be difficult to predict how
voters would behave solely on the basis of information present in
rankings.  There are also situations in all of the ranked methods where
information about the strength of voters preferences is needed to be
able to predict how they will actually vote (when it would be reasonable
to use order-reversal, etc.)

For this purpose, no benchmark is needed for sincere ratings to be
useful.


2)  To allow for a determination of who "should" win.  This implies some
sort of standard or benchmark.  I doubt whether there will be much
agreement on which standard would be correct, but the prospects are no
worse than for agreement on an actual election method.  It seems to me
that if we are going to argue about which election method chooses the
"right" winner, there must be a way to define which winner is the right
one independent of the method.  Since we have the sincere ratings, there
is no need to worry about things like resistance to strategy, and we
should be able to come up with a more accurate standard than is possible
in a real election method -- shouldn't we?

***

A.  SINCERE SCENARIO:

      1.00 .90                       .10  0
45      A                              B  C
15      B   C                             A
40      C                              B  A

-----
D-  How many times must I repeat myself ? -- There will be polls whatever 
method is being used.  

A choice either gets majority acceptability or it does not (i.e. the same as 
in voting on legislative issues as in voting for executive/ judicial 
candidates).   

Whatever method is used, minority choices (and their supporters) will attempt 
to strategize to defeat some choice based on such polls (with their counter- 
strategizing conspiratorial/ evasive/ lying voters).  

A single winner election method will thus operate on the votes as cast (not 
on an infinite number of replayed strategized votes) to produce "a" winner 
(who is thus the "right"/"correct" winner).

As to the scenario, only C has the acceptability of a majority of the voters 
above 0.50.     C should win (without having to do the other math).   

It is only where there are 3 or more choices with majority acceptability 
("approval") and no head to head (Condorcet) winner that there is a problem 
in picking "a" winner.    

Because of the majority acceptability factor, a majority should be able to 
survive whatever specific choice is chosen (especially if recalls are 
possible in the case of elective officers).   Parts of the minority will be 
unhappy to various degrees -- such is life (as in the members of defeated 
sports teams, bankrupt business owners, etc.).

If sincere ratings were being used, the obvious strategy by candidates would 
seem to be to ask their supporters to give 1.00 votes to such candidates and 
0.0 to all other candidates -- ending up with approval voting.  

A simple ratings method would be to have a maximum rating of double the 
number of choices (N) with the medians of the choices getting above (N+1)/2 
going head to head using the rankings.  Example-

5 choices A to E, max =10, min = 1, average 5.5
(i.e. all choices could be rated 6 to 10 (above average) or 1 to 5 (below 
average)

voter 1   voter 2  etc.
D 10         C 10
B  9          E  8
C  7          A 5
E 4            B 3
A 2           D 1
Assume B, C and E have medians above 5.5.   They would go head to head using 
the relative rankings.  If there was no head to head winner, then a 
tiebreaker might simply be the highest median.