## "Naive exaggeration," "Duopoly," and "cash dominance" (Executive summary)

The "naive exaggeration" voting strategy (NES) is:

The voter identifies the two candidates A & B she considers most likely to win. She then votes maximum-allowed-vote for A and minimum-allowed-vote for B (or vice versa) trying naively to "maximize her vote's impact" or equivalently to avoid "wasting" it. If the rules of the voting system permit it, she then also supplies information about additional candidates. (She may do that honestly or strategically, it will not matter for our purposes.)

Empirical fact: Between 80% and 95% of the voters in Australia (which uses rank-order voting systems) employ NES in the sense that 80-95% of the ballots rank the two major parties either {top, bottom} or {top, 2nd-to-bottom}. (Full ranking of all candidates is compulsory in most of Australia, and in House races typically there are 7-8 candidates, and in Senate races more.) Call the latter "NES2."

• With plain plurality voting, if at least 2/3 of the voters employ either NES or NES2 (or any mixture), then one of the top-2 will always win. It is mathematically impossible for a third-party candidate to win.
• With Instant Runoff (IRV) voting, if at least 3/4 of the voters employ either NES or NES2 (or any mixture), then one of the top-2 will always win. It is mathematically impossible for a third-party candidate to win.
• With Bucklin or Condorcet voting (both with strict rank-order ballots), if all voters employ NES and/or NES2, then one of the top-2 will always win. It is mathematically impossible for a third-party candidate to win. However, if, say, only 80% employ NES/NES2 then it becomes mathematically possible, but unlikely, for a third-party candidate to win.
With Condorcet, this happens if the two majors have very near-equal support, both below 50%.
• In contrast, with range and approval voting, even if 100% of the voters employ NES (or NES2) it still is quite possible for third-party candidates to win. Indeed in a simple probabilistic model of elections with equal candidate quality, third-party candidates win at least 22.9% of the time (the precise percentage depends on how many run, but it always is ≥22.9%). Note that 22.9% is a lot better win-percentage than 0.

These facts suggest two conclusions:

1. Plain plurality and IRV definitely will lead to duopoly. Condorcet and Bucklin with strict rank-order ballots perhaps will yield duopoly. Range voting is the most likely to escape duopoly (more likely than approval voting due to the nursery effect).
2. Cash is likely to be supreme in plain plurality and IRV voting. If the top two candidates in terms of advertising budgets are thought by voters to be the two most likely to win, then with enough NES/NES2 voters they will win (regardless of how the voters perceive their quality as candidates). This in turn will convince donors to give money only to the top two, amplifying the effect. It's about convincing voters you are top-2-most-likely to win, not about convincing them you are the best. But with range voting, quality, not cash, has the opportunity to matter.

Math behind 75% & 66.7% thresholds (preliminary page, under construction)

Math about NES, such as the magic number "22.9%" (preliminary page, under construction)

Cash dominance page (preliminary page, under construction)