Why would they be? Because they are asked to express the support they give to all candidates instead of choosing one? Because they would “exaggerate” the mention they assign to their first choice and “reject” all others? This is dubious at best, since the overwhelming majority of voters specifically want to express themselves when they vote.
By attributing “rejected” to all but one candidate, a voter would actually deprive himself of providing nuances about his second or third choices. If he cheats, it is because he thinks his favourite candidate does not have a solid chance; so why lose the possibility to indicate which of the other candidates would be his “second favourite” or “third favourite”.
Moreover, by attributing an exaggerated “excellent” to his favourite candidate instead of a mention more in line with his true convictions, a voter does not actually affect the result of the vote; at least, unless a full 50% of all voters have a better opinion about the candidate than he does. Likewise, by attributing an exaggerated “rejected” mention to an unpopular candidate instead of a mention more in line with his true convictions, a voter does not affect the outcome of the vote; unless a full 50% of all voters have a worse opinion about this candidate than he does. For these reasons and because Majority Judgment does not rely on averages, even if voters did cheat by exaggerating their opinions, the actual impact would be minimal.
Let’s imagine a classic case with two candidates, A and B, both receiving “good” as their majority mention. Imagine that a voter, Theo, prefers A over B. Theo may be tempted to give A an “excellent” mention and “reject” B. In most cases, this will have no impact on the outcome. Indeed, there are two possibilities:
- Case 1: Theo thinks that A deserves “good” or more and that B deserves “fair” or less. This will be the case for the vast majority of voters preferring A over B. In this case, Theo’s exaggeration would have no impact using Majority Judgment.
- Case 2: Theo gives both candidates (1) “fair” or less or (2) “good” or more. But then, Theo does not have a strong enough motivation to exaggerate and will probably prefer to vote honestly. Indeed, in case 1, he does not like either candidates and, in case 2, he actually likes both candidates. Finally, even if he is convinced to cheat, lowering B’s mention in case 1 or increasing A’s mention in case 2 will not change anything. This further limits voters’ ability to cheat.
This reasoning is generic. A theorem (ADD LINK to the MIT Press Book) further shows that, in the rare cases where a voter may actually have influenced the outcome of the election by cheating, the scope of this influence is very limited: if the voter can help his favourite candidate, he cannot hurt his competitors, and if he hurts the competitors, he cannot help his favourite candidate.
Conversely, with the grading vote, exaggerating always has an effect and a potentially potent one. Increasing Candidate A’s grade from 7 to 10 directly increases his average, and lowering B’s grade from 5 to 0 lowers his average. This explains why, in all simulations, grading vote is the most susceptible to manipulation and Majority Judgment is the least (see chapter 19 of the book [ADD LINK]).
With Majority Judgment, the optimal strategy for the vast majority of voters is simply to vote honestly because it gives them a better voice in the election and because exaggerating will not change the winner anyway.