# [EM] IRV vs BRGL

Susan Simmons suzerainsimmons at outlook.com
Wed Jul 7 19:00:04 PDT 2021

```IRV and BRGL are both loser-elimination methods ... the first step of each method is to eliminate the least desireable candidate ... subsequent steps eliminate the least desireable candidates from among those not eliminated previously.

The methods differ only on the question of how desireability (or lack thereof in the estimation of the voters) is reflected in the "counting of" their voted ballots.

In particular, suppose the ballots can be summarized by the table

36 A>C>B
13 C>A>B
17C>B>A
34 B>C>A,

which could happen if, for example, the candidates were distrbuted more or less evenly along a left-right spectrum with C located roughly halfway between A and B.

Note that C is the Plurality Loser, the favorite of the fewest voters, hence the candidate deemed least desireable according to IRV, and eliminated by IRV in the first round ... followed by a victory of B over A in the final round.

On the other hand C is preferred by 64 percent of the ballots over A, and by 66 percent of the ballots over B.  So how can we explain the superiority of B over C to the supporters of C? (or even to the supporters of A, all of whom prefer C over B)

Speaking of the supporters of A ...they were promised by IRV promoters that if their first choice A were to lose, then their vote would transfer to their second choice C ... why didn't that happen?

This basically is what soured Burlington voters against IRV in 2008.  Now IRV has a new name being promoted to a new generation of voters.

So back to our question ... whom does BRGL consider to be least desireable according to the ballots?

Answer ... candidate B because in the pairwise contest between B and C, candidate B only gets 34 percent of the votes, while A never gets fewer than 36 percent of the votes in any pairwise contest, and C never gets fewer than 64 percent of the votes, as we have already seen.

The ballots, when seen from this less superficial point of view, seem to reveal B as the least desireable of the three. The BRGL method therefore eliminates B in the first round, and C beats A in the last round.

So IRV elects B while BRGL elects C. Note that the BRGL winner beats the IRV winner pairwise ... a majority of the voters prefer the BRGL winner over the IRV winner.

Is this a fluke? No. It is not unusual (in random simulations) for the sincere Condorcet candidate to be squeezed out by a wall of other candidates surrounding it, thereby shielding it from receiving first place votes from its deeper supporters. Sophisticated supporters can counteract this squeeze effect by insincerely voting their second choice ahead of their favorite, the same lesser evil strategy prevalent in Plurality voting that IRV was suppose to fix.

In the above example,  if a few of the A>C>B voters were to (insincerely) vote their lesser evil C over A (switching to C>A>B) their IRV result would improve (an improvement according to both their sincere and lesser evil ballots) from B to C... in general the Condorcet candidate will be a Nash equilibrium rewarding sophisticated voter manipulations when they are in possession of reasonably complete preference information. In summary, sphisticated manipulation of IRV would tend to elect a CW more often than sincere ballots would.

This fact gives the lie to claims of IRV promoters that IRV obviates the necessity of lesser evil voting ... in fact, every deterministic ranked preference method is more or less vulnerable to incentives for reversing (or collapsing) sincere ballot preferences ... IRV more, Condorcet methods less.

Sent from my MetroPCS 4G LTE Android Device
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20210708/fa8abaa2/attachment-0001.html>
```