<p>Let <span class="math-container">$X$</span> be the set of alternatives, and <span class="math-container">$(R_i)_{i\in N}$</span> a profile of partial orders for <span class="math-container">$n= \#N$</span> individuals. I make the assumption that those partial orders are so that they all give rise to one best alternative to ensure some kind of rationality at the individual level, but feel free to weaken/strengthen those assumptions as my question is about the existence of such rules in the literature and not about individual preference models.</p>
<p>I was wondering whether there were a known preference aggregation rule that satisfies the following property: if <span class="math-container">$A\in X$</span> is the alternative that is most frequently the best alternative among the preference profile, then it will also be the best at the collective level.</p>
<p>My question is a denomination/reference question: does their properties/philosophical values have be studied?
If so, is there a name for a rule satisfying such a property? What are some example of such a rule? And if we apply this rule not only to the best, but to the second best, third best and so on... does it have a name?</p>

CC BY-SA 4.0
2024-04-03T13:14:45.653Z
Sorry but isn't your description of the rule characterization of the social ranking itself? Rank the most frequent first choice as first, second most frequent as second, etc.
Giskard
CC BY-SA 4.0
2024-04-03T14:51:03.217Z
@Giskard Indeed, the extension is. I will edit the question to make it clearer. Do you happen to know such a rule? (and thus a name?)
MiKiDe
CC BY-SA 4.0
2024-04-08T06:21:25.803Z
I think this is called plurality voting. Of course, this system does not guarantee that each person votes for the person top ranked in their preference; as it is not strategy proof.
tdm
<reference-request><preferences><social-choice>
Preference aggregation rules that satisfy the property that the most frequent best alternative is the collective best alternative?
MiKiDe
# Preference aggregation rules that satisfy the property that the most frequent best alternative is the collective best alternative?

(Asked by: username_0 on 2024-04-03)

Let $X$ be the set of alternatives, and $(R\_i)\_{i\in N}$ a profile of partial orders for $n= \#N$ individuals. I make the assumption that those partial orders are so that they all give rise to one best alternative to ensure some kind of rationality at the individual level, but feel free to weaken/strengthen those assumptions as my question is about the existence of such rules in the literature and not about individual preference models.

I was wondering whether there were a known preference aggregation rule that satisfies the following property: if $A\in X$ is the alternative that is most frequently the best alternative among the preference profile, then it will also be the best at the collective level.

My question is a denomination/reference question: does their properties/philosophical values have be studied?
If so, is there a name for a rule satisfying such a property? What are some example of such a rule? And if we apply this rule not only to the best, but to the second best, third best and so on... does it have a name?

**Tags:** reference-request, preferences, social-choice

> **Comments:**
> **username_1**: Sorry but isn't your description of the rule characterization of the social ranking itself? Rank the most frequent first choice as first, second most frequent as second, etc.  
> **username_0**: @username_1 Indeed, the extension is. I will edit the question to make it clearer. Do you happen to know such a rule? (and thus a name?)  
> **username_2**: I think this is called plurality voting. Of course, this system does not guarantee that each person votes for the person top ranked in their preference; as it is not strategy proof.  

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## 0 answers

