[EM] Head-to-head: Schulze vs. MTM (majoritarian Tideman)

[Bart Ingles]

Steve Eppley wrote:
> 
> The following data, calculated by software written to simulate
> many voting methods, supports my contention that MTM dominates
> Schulze in the head-to-head comparison of whether voters would
> prefer one's winners more than the other's winners.
> 
> Norm Petry posted some of his own data a few days ago, but I
> believe his data is erroneous. (See my reply to Norm in a
> message being posted separately.)  In particular, Norm's data
> showed Schulze best when there are 3 alternatives, but my
> reckoning is that, when there are 3 alternatives, the Schulze
> winner never beats the MTM winner or the IBCM winner or the
> PC(wv) winner. (As Markus noted a year ago, when there are 3
> alternatives, the Schulze method chooses the same as PC(wv).)

Could the difference have to do with the way random ballots are
generated?  Randomly generated rank orders, and rankings based on
randomly generated voter positions on one or more axes, *should* produce
different election results.