[EM] The Hippopotamus Logic

[Steve Eppley]

Donald D wrote:
>I've only been on this list for less than a year.

This is true for all of us.  The EM list was launched in February
1996, as a spin-off of the ER list after some ER subscribers objected
to receiving messages in which methods were debated.  (Rob Lanphier,
the EM list-owner, also wants the EM list to be used to develop
educational materials about voting methods--see the list's welcome 
message.)

>>These standards include majority rule, and getting rid of the
>>lesser-of-2-evils (LO2E) problem. It's been amply demonstrated,
>>more than once, that Condorcet meets these standards & criteria,
>>and that IRO fails them in a big way.
>
>Thank you - I often would wonder what (LO2E) meant - as I waded
>through the pages of this list.

Does your email browser provide a search function?  If so, can you 
search an email folder with the search ordered by message date?

>>If a full majority of all the voters indicate that they'd rather
>>have A than B, then if we choose A or B, it should be A.
>>
>>Condorcet's method is the only proposed method [that] respects that
>>principle, meaning that it will never unnecessarily violate it.
>
>Would you show me an example of IRO violating the rule of majority?

The 46/20/34 example shows IRO violating it.  We've discussed this
already, but here goes again:
   46:ABC
   20:B
   34:CBA
A majority (54) indicated they'd rather elect B than A, yet IRO
elects A.  If there's some principle which makes you think this 
is a "necessary" violation, I'd like to hear it.

Candidate A is the *only* candidate over whom a majority ranked
another, yet IRO elects A.

Candidate B would defeat A or C if it were a two-candidate race,
yet in IRO B is the big loser, being eliminated right away.

In a two-candidate race between A and B, B would win 54 to 46.
If C chooses to run, s/he "spoils" the election for B.  Presumably 
candidate C would rather have B win than A.  So C may well decide 
not to compete.  Do you like a method which squelches candidates, 
or would you prefer one which performs better on the "No Spoilers"
standard:

   If candidate X would be elected when Y is not a candidate, 
   then X or Y should be elected if Y is a candidate (assuming 
   the voters don't alter their relative orderings of the 
   non-Y candidates).

The voters who sincerely prefer C more than B have to decide whether
it's more important to defeat A than express their support for C--
the LOE dilemma.  We know many voters will decide that defeating A is 
more important.  Do you like a method which suppresses voters' most 
important political speech this way, by forcing them to choose 
between defeating the greater evil or showing support for their true 
favorite?

If you're hoping to promote multiparty democracy, then in elections
which can't be prop rep (because they're single-winner) you'll want
to advocate a voting method which performs well on the LOE, No
Spoilers, and Majority Rule standards.  (These standards emphasize
different properties, but they're really just aspects of the same 
phenomenon.)

IRO is satisfactory at eliminating fringe candidates who have little 
support and transfering their supporters' votes:

   A       B       C
       |   V   |
       |VVVVVVV|
    VVV|VVVVVVV|VVV
  VVVVV|VVVVVVV|VVVVV

But it's not satisfactory at dealing with the more important
scenario where there are significant candidates slightly left and
right of center. In these common scenarios, the slightly off-center
candidates take away most of the first choice votes from the center
candidate:

         A B C
          |V|
       VVV|V|VVV
    VVVVVV|V|VVVVVV
  VVVVVVVV|V|VVVVVVVV

The V curve shows a possible voter distribution, in these cases
something like a bell-shaped curve.  The '|' demarcates the most
preferred candidate of the voters: A is most preferred by the voters 
at the left, C is most preferred by the voters at the right, and 
B is most preferred by the slim number of voters in the tall but 
skinny center.

So in practice, the candidates and voters will have major strategy
problems when IRO is used.  Candidates will try to position
themselves slightly left or right of the one in the center, and the
one in the center will seek to "jump" over a neighboring candidate
to capture the first choices of a wing (plus the early transfers 
from the tiny fringe candidates, if there are any).

Here's an example which isn't as simple as the 46/20/34, but perhaps 
you'll appreciate its greater realism.  It illustrates the same 
problem.  (In my opinion, it's easier to understand the simpler 
example, but I'll defer this time to Donald's request.)

   2:A
  36:AB
   8:ABC
   7:BA
   6:B
   7:BC
   8:CBA
  24:CB
   2:C
 ---
 100

  IRO eliminates B first and elects A as in the simpler example,
  even though a majority (52 = 7+6+7+8+24) prefer B more than A.

IRO can be salvaged, and Condorcet can be slightly improved to
better deal with some rare scenarios, by modifying the method so it
iteratively bumps up candidates in rankings when a worse candidate 
is leading.  You can think of this as "smart ballots" which modify
themselves as needed to carry out the implied wishes of the voters--
effectively "approving" the voter's lesser of evils as much as the
voter's true favorite if needed to defeat the voter's greater of 
evils.  (This improvement comes at a cost of added complexity, though.)  
For instance, if candidate A is leading after the first iteration,
then the ballots B>C>A and C>B>A would be adjusted to B=C>A and all
the ballots would be re-tallied.  

Try this "modified-IRO" in the 46/20/34 example above and you'll
find that even though A leads after the first round (the plain IRO
result), B is the eventual winner.  The modification takes the LOE
dilemma away from the C>B>A voters since they can trust the tally 
to "correct" their ballots to C=B>A if this is needed to defeat A. 

We haven't extensively studied this modification, however.  It 
appears to work well, but this conclusion may not be final.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)