## Some arguments why IRV, Condorcet methods, and "nondegenerate weighted positional" voting systems all will lead to self-reinforcing 2-party domination, just like the plurality system

In "non-degenerate weighted-positional" voting systems such as Dabagh, Borda count, or the (probably better) system used on the island of Nauru, the best voter strategy essentially always is to exaggerate and rank the two perceived frontrunners (i.e. the two candidates whom the voter believes are most likely to win the election) max and min.

In the IRV system, it sometimes is and sometimes is not the case that this is the best voter strategy. We know it sometimes is the case, because here is an example and here another. We know that (asymptotically 100% of the time) such exaggeration is at least as strategically good as honest-voting for at least one kind of voter in a "large random electorate" mathematical model, because of this proof.

Now whether or not such exaggeration is always strategically best, given that it is known sometimes to be best, and other times known to be at least better strategically than being honest (even if non-best) a lot of members of the Public will do it (regardless of what the best strategy is). If enough members of the Public do this, then 3rd parties can never win under IRV. (Because: they will be eliminated in early rounds.) I conjecture that this is the reason, or at least part of the reason, that all three IRV countries are 2-party dominated, just like plurality countries.

Now the preceding two paragraphs, including the example (but with this different proof) remain completely true if everywhere you see the word "IRV" you substitute "Condorcet with preference rankings as votes," except for the caveat that there are as yet no Condorcet countries. (The reason 3rd parties cannot win under Condorcet if voters behave this way is, that one of the two major-party candidates is guaranteed to be a Condorcet winner.) This all makes it plausible to me that the exact same thing would happen under Condorcet: also 2-party domination.

(Political parties have not yet become important on Nauru, so we cannot yet judge if that place will become two-party dominated. There are only about 12 thousand inhabitants so political parties may not really be useful there.)

This all should be disappointing news for third-parties who had hoped that using IRV, weighted-positional, or Condorcet methods would enable them to rise above being permanent roadkill. Those systems naively may sound like they give third parties more of a chance. But in fact, in the case of IRV we know that naive perception is wrong. It almost certainly is also wrong in all nondegenerate weighted positional systems and plausibly also for Condorcet methods.

So we suggest to third parties that they advocate range voting!