Editing Strategic voting (section)

=== Cardinal single-winner voting ===
{{See also|Score voting#Strategy|Approval voting#Strategy}}
Most cardinal, single-winner voting systems in large elections encourage similar strategies:

# Calculate the expected (average) utility of the election result (the average [[utility]] if the election was repeated many times).
# Top-rate all candidates with above-average utility, and bottom-rate all candidates with below-average utility.

Such a strategy involves "semi-honest exaggeration". Unlike in most voting systems, voters rarely (if ever) have an incentive to lie about which of two candidates they prefer, which makes such far milder than under other voting systems. Voters exaggerate the difference between a certain pair of candidates but do not rank any less-preferred candidate over any more-preferred one. This form of exaggeration has an effect whenever the voter's honest rating for the intended winner is below that candidate's median rating; or when their honest rating for the intended loser is above it. In other words, half of voters will have an incentive to strategize, while half will not.

Typically, this would not be the case unless there were two similar candidates favored by the same set of voters. A strategic vote against a similar rival could result in a favored candidate winning; although if voters for both similar rivals used this strategy, it could cause a candidate favored by neither of these voter groups to win.

[[Michel Balinski|Balinski]] and Laraki noted that under majority judgment, many voters have no opportunity or incentive to use strategy. They argued based on a simulation that the highest median methods minimized the number of voters with an incentive to misrepresent their opinions, among the methods they studied.<ref name=mjrank>{{cite book | last1=Balinski | first1=M. L. | last2=Laraki | first2=Rida | title=Majority judgment: measuring, ranking, and electing  | publisher=MIT Press | publication-place=Cambridge, Mass. | date=2010 | isbn=978-0-262-01513-4}}{{page?|date=February 2025}}</ref>

Strategic voters are faced with the initial tactic as to how highly to score their second-choice candidate. The voter may want to retain expression of a high preference of their favorite candidate over their second choice. But that does not allow the same voter to express a high preference of their second choice over any others.

In [[approval voting]], because the only option is to approve of a candidate or not, optimal strategic voting rarely includes ranking a less-preferred candidate over a more-preferred candidate. However, strategy is in fact inevitable when a voter decides their "approval cutoff". [[Steven Brams]] and [[Dudley R. Herschbach]] argued in a paper in ''[[Science (journal)|Science]]'' magazine in 2001 that [[approval voting]] was the method least amenable to tactical perturbations.<ref name="Heschbach2">{{cite journal |last1=Hershbach |first1=Dudley |last2=Brams |first2=Steven |date=2001-05-25 |title=The Science of Elections |url=https://www.science.org/doi/full/10.1126/science.292.5521.1449 |journal=Science |volume=292 |issue=5521 |page=1449 |doi=10.1126/science.292.5521.1449 |pmid=11379606 |access-date=2024-05-10}}</ref>

Balinski and Laraki used rated ballots from a poll of the [[2007 French presidential election]] to show that, if unstrategic voters only approved candidates whom they considered "very good" or better, strategic voters would be able to sway the result frequently, but that if unstrategic voters approved all candidates they considered "good" or better, approval was the second most strategy-resistant method of the ones they studied, after majority judgment itself.<ref name="mjrank" />