# [EM] The lead method: Smith, DMTBR, and almost monotone. Salvageable?

Kristofer Munsterhjelm km_elmet at t-online.de
Tue Mar 16 03:27:23 PDT 2021

```On 03/03/2021 13.52, Kristofer Munsterhjelm wrote:
> Let's call the method Plurality Benham (or the lead method, from "Pb").
> It is just Benham, except that the elimination order is fixed at the
> start of the run as (the reverse of) the Plurality order.

Replying to myself, but I just realized that the lead method is
summable. That makes it the only method I know of that passes all of
Smith, DMTBR, and summability.[1]

Whether some subset of the candidates has a Condorcet winner (when
considering only those candidates) can be determined from the Condorcet
matrix. And Plurality is obviously summable. So the method, as a whole,
is also summable.

This is surprising, because I thought that DMTBR is sufficiently strict
that you'd need a superpolynomial amount of information to keep the
method from being fooled, if it also were also to pass Condorcet. Not
that I'm complaining at being proven wrong!

-km

[1] For that matter, it's the only method that passes the strict
interpretation of DMTBR and summability, at all. Plurality is obviously
completely immune to burial, but it doesn't elect from the smallest DMT set.
```