# [EM] A family of easy-to-explain Condorcet methods

Daniel Carrera dcarrera at gmail.com
Thu Jul 1 20:16:45 PDT 2021

```On Thu, Jul 1, 2021 at 5:51 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> You probably need to define the list-creating procedure and explicitly
> refer to striking candidates off the list, so as not to confuse the
> method with IRV. I did a cursory check of Reddit and cmb3248 said "IRV
> is literally the same thing [as Pb] except instead of Condorcet winners
> it uses majority winners, something people already get". The
> remove/eliminate distinction seems to be a subtle one that not everybody
> gets.
>

Indeed, I'm sure most people would say that "remove" and "eliminate" are
synonyms. Even now I honestly don't understand why you assign them
different meanings (a dictionary says that they're synonyms). I simply
accepted the different meanings that you assigned to them for the sake of
communication.

> In a three-cycle, Pb would elect the candidate among the top two who
> beats the other one pairwise - kind of like top-two runoff within the
> Smith set, now that I think of it.
>
> It's possible that in a cycle situation, a party A can split its vote so
> that instead of the Plurality ranking being A>B>C, it becomes B>C>A1>A2,
> and then the clones are kicked off the list early, after which B beats C
> pairwise and wins.
>

That's a bit similar to how Minimax is not clone independent either. I
think a similar example shows that Pb is not ISDA either. Imagine that A2
is not quite a clone but is similar enough to siphon a few first-choice
votes. So the Smith set is still {A,B,C} but Plurality now ranks 'A' lower.

I suspect that in practice Pb would work great. I once read that >90% of
elections have a Condorcet winner anyway (I think that came from Tideman
but I forget). For those that don't, I never expect to see a 4-cycle with
two clones. For a 3-cycle Minimax and Ranked Pairs will both break the
cycle at the weakest link, which I think is obviously the best choice. Pb
won't always do that, but I just made a handful of 3-cycle elections at
random and Pb seems to agree with Minimax & RP more than half the time. So
I would be very surprised if any of this ever came up in an election.
Contrast this with IRV where its issues can show up easily and we already
have the example of Burlington where IRV obviously chose the wrong
candidate.

In any event, it's a failure that IRV proponents will use for all that
> it's worth (just like we hold IRV's monotonicity against it).
>

Yeah.

Daniel
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