[EM] Summary of order reversal software output

[Steve Eppley]

In another message (my reply to Markus about JITW) I mentioned 
that I'd post this summary.  There's some more info about 
this in that JITW message.

Below is a table of order reversal scenarios in 3-alternative 
elections, given various voting methods.  (Hopefully I haven't 
written buggy software.)  The software which generates it also 
examines the incentives of the patsy candidate to withdraw if 
given the opportunity by JITW to foil the reversal.  And it 
calculates a variety of stats which might be of interest 
(e.g., the number of scenarios where the reversal winner's 
sincere Borda score is worse than the sincere winner's 
sincere Borda score).

The software produces more files, including the databases of 
scenarios, but it seems inappropriate to post it all here.

It's pretty easy for me to code additional pairwise methods.  
But to test for reversal scenarios in non-pairwise methods such 
as Instant Runoff, the software would need to be partially 
rewritten since the reversal strategy in those methods is 
not ABC -> ACB.  (In Instant Runoff, the successful reversal 
strategies are ABC -> CAB and ACB -> CAB, which can defeat B 
by elevating C's IRV score ahead of B's.  Don't believe people 
who claim that reversal cannot succeed in Instant Runoff.)

I've also written software which finds the intersection of the 
reversal scenarios of two methods.  I wrote this because it 
might make sense to use a "combo" method, in which the voters' 
preferences are tallied using two different algorithms, and the
overall winner is the pairwinner of the two algorithm-winners.  
If the reversal intersection of two algorithms is small, combining 
them might thwart reversal better.  (But we'd have to also check 
for scenarios where reversal succeeds in one algorithm and the 
"patsy" wins in the other, since the reversal winner defeats 
the patsy pairwise.)

I intend to write software to find the scenarios where truncation
succeeds, and to intersect those with the scenarios where reversal 
succeeds, to help provide a more quantitative answer on whether
voters would have an incentive to rank only their favorite.

--Steve
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The following is best viewed using a monospace (nonproportional) 
font and with wordwrap turned off, in my opinion.

Method "VA" is Condorcet{VotesAgainst}.  
Method "Copeland" is Copeland//Plurality.
Method "Schz" is Schulze's Method.  Though it appears to perform 
worse than VA on most stats, it might perform better with more 
than 3 alternatives.

Methods TC1 and TC2 haven't been discussed in this maillist.  
They perform well at reducing the number of scenarios where reversal 
can succeed, at least in 3-alternative elections.  Their "sincere
Borda" and "Thwarted Majority" stats appear worse than other methods'
but it's unclear if this is a fair comparison; for example the 
75 worst VA scenarios might be as bad or worse on these stats as 
the 75 TC1 scenarios.

 VOTERS METHOD     CWS REVERSALS JITWFOILED BACKFIRES MINREV MINREVS JITWMINREV BORDAWORSE MINRBORDA FAILSDSC BORDAWORST BORDAAVG THWARTMAX THWARTAVG

     17 TC1       1254        75         57         0      1      51         39         72        48        0       0.46     0.78      88.2      63.3
     17 TC2       1254        79         38        13      1      26         12         65        18       15       0.64     0.88      70.6      57.6
     17 Cope      1254       239        239         0      1      51         51        160        18      164       0.70     0.94      58.8      54.2
     17 Schz      1254       409        317         0      2      84         56        278        28        0       0.71     0.94      64.7      54.0
     17 VA        1254       292        230         0      2      56         39        161         0        0       0.75     0.97      58.8      53.7

     18 Cope      1584       140        140         0      2      34         34        116        21       92       0.71     0.90      61.1      56.5
     18 Schz      1584       226        191         0      3      56         43        191        36        0       0.72     0.90      61.1      56.3
     18 VA        1584       154        132         0      3      35         28        119        15        0       0.76     0.93      61.1      56.1

     33 Cope     27132      5788       5739         0      1     680        673       4008       250     3892       0.66     0.94      63.6      54.0
     33 Schz     27132      9749       6703         0      2     680        368       6523       120        0       0.69     0.95      63.6      53.5
     33 VA       27132      8219       5662         0      2     560        308       4993         0        0       0.71     0.97      63.6      53.3

Key to table:
CWs        = number of scenarios where B is sincere condorcet winner
                but not the favorite of a majority.
Reversals  = number of scenarios where reversal can elect A.
                (Smaller is better.)
JITWFoiled = number of scenarios where reversal would probably be
                foiled by C voluntarily withdrawing. (CBA/C > 60%)
                (Larger is better, but this is relative to Reversals.)
Backfires  = number of scenarios where reversal can succeed but too much
                reversing backfires by electing C.  
                (Larger is better since it deters reversal.)
MinRev     = minimum number of reversers needed to reverse at least
                one scenario.  (Larger is better.)
                (I don't know if this stat matters.  It's probably
                1 to 3 regardless of how many voters there are.)
MinRevs    = number of scenarios where the number of reversers needed
                to successfully reverse equals MinRev.
                (Smaller is better.)
                (I don't know if this stat is useful, especially
                since it depends on the method's MinRev.)
JITWMinRev = number of MinRevs scenarios where reversal would probably
                be foiled by C voluntarily withdrawing.
                (Larger is better, but this is relative to MinRevs.)
BordaWorse = number of reversal scenarios where A's sincere Borda score
                is worse than B's.  (Smaller is better.)
MinRBorda  = number of MinRevs scenarios where A's sincere Borda score
                is worse than B's.  (Smaller is better.)
FailSDSC   = number of scenarios where reversal isn't thwarted by
                by BAC -> B>A=C truncation.  (Smaller is better.)
BordaWorst = smallest ratio of A's sincere Borda score to B's.
                (Larger is better.)
BordaAvg   = average ratio of A's sincere Borda score to B's.
                (Larger is better.)
ThwartMax  = largest percentage of voters who ranked B ahead of A.
                (Smaller is better.)
ThwartAvg  = average percentage of voters who ranked B ahead of A.
                (Smaller is better.)