# Preference terminologies

I am reading one paper by [Maskin et al. 1979] 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.

• That would be Dasgupta et al, if writing complete references is too much work. Mar 3, 2022 at 19:22

$$R,P,I$$ 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 ($$a \sim b$$)