Does IRV elect candidates with depth and breadth of support?

Introduction

Proponents of Instant Runoff Voting (including its truncated form, called “Ranked Choice Voting” or “RCV” for short) often claim that IRV elects candidates with both depth and breadth of support. For example:

“RCV elects candidates that elicit both passionate and broad support, both of which are necessary qualities in a leader.”
California RCV proponent in a letter to the editor

Counterexample

The following 5-candidate RCV election is won by candidate Z.

 # of voters  their ranking
 1  A>Z
 2  Z
 2  B>A>Z
 4  C>A>Z
 8  D>C>A

But note that candidate C has twice as many first-place rankings as Z (4 versus 2), and is preferred to Z by a 71% majority (12 of the 17 voters).C has greater depth and breadth than Z, but RCV still elects Z.   And A is preferred to Z by an 88% majority (15 of the 17 voters).

Vague metric

Beyond the fact that IRV does not actually ensure the virtues touted in the above quotation, another problem is that these virtues have not even been specifically described. How high does a candidate have to be ranked on what number of ballots in order to qualify as having elicited passion or having support that is “broad”?

Better metric

We propose a better metric, called Bayesian regret, which measures the average voter satisfaction associated with a given voting method. By its very nature, Bayesian regret simultaneously incorporates depth and breadth.

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