<p><span class="math-container">$R,P,I$</span> are preference orderings. Perhaps you have seen the notation <span class="math-container">$\succeq$</span> for preference orderings?</p>
<p>To say <span class="math-container">$a R_i b$</span> means <span class="math-container">$a$</span> is at least as good as <span class="math-container">$b$</span>. (<span class="math-container">$a \succeq b$</span>)</p>
<p><span class="math-container">$a P_i b$</span> means <span class="math-container">$a$</span> is strictly preferred to <span class="math-container">$b$</span>. (<span class="math-container">$a \succ b$</span>)</p>
<p><span class="math-container">$a I_i b$</span> means <span class="math-container">$a$</span> and <span class="math-container">$b$</span> are indifferent to one another (<span class="math-container">$a \sim b$</span>)</p>

CC BY-SA 4.0
2022-03-03T20:50:40.847Z
2022-03-03T20:50:40.847Z
Walrasian Auctioneer
<p>I am reading one paper by <a href="https://scholar.harvard.edu/files/maskin/files/the_implementation_of_social_choice....pdf" rel="nofollow noreferrer">[Maskin et al. 1979]</a> and cannot figure out some notations. Specially, they defined some states of nature <span class="math-container">$A$</span>, and each player in the player set <span class="math-container">$I$</span> has some preferences over the states of nature. The preference is just some logical orderings of <span class="math-container">$A$</span>. For example, let <span class="math-container">$A = \{a, b\}, I = \{1, 2, 3\}$</span>. Let each player <span class="math-container">$i$</span> have two preferences <span class="math-container">$R_i, R_i^{'}$</span>, i.e. <span class="math-container">$R_1 = [a, b], R_1^{'} = [b, a], \cdots, R_3 =[a, b], R_3^{'} = [b, a]$</span>.</p>
<p>Then the paper uses some notations <span class="math-container">$a R_i b$</span>, <span class="math-container">$a P_i b$</span>, and <span class="math-container">$a I_i b$</span> without introducing the meaning of these notations. I guess that the meaning of <span class="math-container">$a R_i b$</span> is that <span class="math-container">$a$</span> is higher/preferred than <span class="math-container">$b$</span> in the logical ordering represented by <span class="math-container">$R_i$</span>. But what do <span class="math-container">$P$</span> and <span class="math-container">$I$</span> mean here? Are they some terminologies in the Economic literature, or are they related to this specific paper? Unfortunately, I could not find any formal definition of these <span class="math-container">$a R_i b$</span>, <span class="math-container">$a P_i b$</span>, and <span class="math-container">$a I_i b$</span> in the paper... The paper also talks about Pareto efficiency, I am wondering could this <span class="math-container">$P$</span> be related to Pareto efficiency? But I have no idea about what does it mean here with a subscript <span class="math-container">$P_i$</span> and with respect to these two states of nature.</p>

CC BY-SA 4.0
2022-03-03T19:22:30.230Z
That would be Dasgupta et al, if writing complete references is too much work.
Michael Greinecker
<preferences><definition><pareto-efficiency>
Preference terminologies
Francis
# Preference terminologies

(Asked by: username_0 on 2022-03-03)

I am reading one paper by [[Maskin et al. 1979]](https://scholar.harvard.edu/files/maskin/files/the_implementation_of_social_choice....pdf) and cannot figure out some notations. Specially, they defined some states of nature $A$, and each player in the player set $I$ has some preferences over the states of nature. The preference is just some logical orderings of $A$. For example, let $A = \{a, b\}, I = \{1, 2, 3\}$. Let each player $i$ have two preferences $R\_i, R\_i^{'}$, i.e. $R\_1 = [a, b], R\_1^{'} = [b, a], \cdots, R\_3 =[a, b], R\_3^{'} = [b, a]$.

Then the paper uses some notations $a R\_i b$, $a P\_i b$, and $a I\_i b$ without introducing the meaning of these notations. I guess that the meaning of $a R\_i b$ is that $a$ is higher/preferred than $b$ in the logical ordering represented by $R\_i$. But what do $P$ and $I$ mean here? Are they some terminologies in the Economic literature, or are they related to this specific paper? Unfortunately, I could not find any formal definition of these $a R\_i b$, $a P\_i b$, and $a I\_i b$ in the paper... The paper also talks about Pareto efficiency, I am wondering could this $P$ be related to Pareto efficiency? But I have no idea about what does it mean here with a subscript $P\_i$ and with respect to these two states of nature.

**Tags:** preferences, definition, pareto-efficiency
> **Comments:**
> **username_1**: That would be Dasgupta et al, if writing complete references is too much work.  

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## 1 answers

### Answer by username_2 on 2022-03-03. Score: 2 | Accepted answer

$R,P,I$ are preference orderings. Perhaps you have seen the notation $\succeq$ for preference orderings?

To say $a R\_i b$ means $a$ is at least as good as $b$. ($a \succeq b$)

$a P\_i b$ means $a$ is strictly preferred to $b$. ($a \succ b$)

$a I\_i b$ means $a$ and $b$ are indifferent to one another ($a \sim b$)


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