Ignoring your votes (Executive Summary)

Nobody likes to be ignored. But in Instant Runoff Voting, a correct algorithm that computes the winner always ignores (i.e. never looks at) asymptotically 100% of the entries in the rank-order votes. Indeed, always, the algorithm looks at a fraction ≤F of the VC entries (in a V-voter, C-candidate election) where

F ≤ (1+1/3+1/4+…+1/C) / C.
This upper bound tends to 0% when C is made large.

In contrast, with range, approval, Borda, plurality, and Condorcet voting, no correct algorithm can always avoid looking at 100% (or nearly) of the entries in the votes. (However, it certainly can sometimes avoid it, e.g. if the first 51% of the votes examined are all for Lincoln, then with plurality voting we'd know the winner without needing to examine the remaining 49%.)

IRV voters have to ask themselves why they are being asked to fill out a rather large ballot of rank orderings when in fact almost everything they write will always be ignored.

The details

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