<p>Yes. See for example this passage from <a href="https://web.stanford.edu/%7Ejdlevin/Econ%20202/Uncertainty.pdf" rel="nofollow noreferrer">Choice under Uncertainty by Jonathan Levin</a>:</p>
<blockquote>
<h3>2.1  Prizes and Lotteries</h3>
<p>The starting point for the model is a set <span class="math-container">$X$</span> of possible <em>prizes</em> or <em>consequences</em>. In many economic problems (and for much of this class), <span class="math-container">$X$</span> will be a set of monetary payoffs. But it need not be. If we are considering who will win Big Game this year, the set of consequences might be:
<span class="math-container">$$X=\lbrace\text{Stanford wins}, \text{Cal wins}, \text{Tie}\rbrace.$$</span>
We represent an uncertain prospect as a <em>lottery</em> or <em>probability distribution</em> over the prize space. For instance, the prospect that Stanford and Cal are equally likely to win Big Game can be written as <span class="math-container">$p=(1/2,1/2,0)$</span>. Perhaps these probabilities depend on who Stanford starts at quarterback. In that case, there might be two prospects: <span class="math-container">$p$</span> or <span class="math-container">$p'=(5/9,3/9,1/9)$</span>, depending on who starts.</p>
</blockquote>
<p><sub>(not sure what I was thinking yesterday evening. It seems like I completely misunderstood the question)</sub></p>

CC BY-SA 4.0
2020-06-24T21:26:13.823Z
I think they mean lotteries in the MWG sense of uncertain cash flow, not real life lotteries, which are a subset of this.
Giskard
CC BY-SA 4.0
2020-06-25T06:10:17.503Z
@Giskard you are right. if you can come with a better answer please do
Xenusi
CC BY-SA 4.0
2020-06-25T07:04:17.647Z
@Xenusi I think Michael Greinecker's comment is the appropriate answer.
Giskard
CC BY-SA 4.0
2020-06-24T19:48:13.647Z
2020-06-25T07:29:06.037Z
2020-06-25T07:29:06.037Z
Glorfindel
<p>Are &quot;lotteries&quot; in the model for choice under uncertainty not just probability distributions?</p>

CC BY-SA 4.0
2020-06-24T20:22:26.243Z
Usually, yes. Details may vary (finite support or not, countable vs finite additivity...)
Michael Greinecker
<consumer-theory><uncertainty>
Lotteries = probability distribution?
Xenusi
# Lotteries = probability distribution?

(Asked by: username_0 on 2020-06-24)

Are "lotteries" in the model for choice under uncertainty not just probability distributions?

**Tags:** consumer-theory, uncertainty

> **Comments:**
> **username_1**: Usually, yes. Details may vary (finite support or not, countable vs finite additivity...)  

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## 1 answers

### Answer by username_2 on 2020-06-24. Score: 2 | Accepted answer

Yes. See for example this passage from [Choice under Uncertainty by Jonathan Levin](https://web.stanford.edu/%7Ejdlevin/Econ%20202/Uncertainty.pdf):

> ### 2.1 Prizes and Lotteries
>
> The starting point for the model is a set $X$ of possible *prizes* or *consequences*. In many economic problems (and for much of this class), $X$ will be a set of monetary payoffs. But it need not be. If we are considering who will win Big Game this year, the set of consequences might be:
> $$X=\lbrace\text{Stanford wins}, \text{Cal wins}, \text{Tie}\rbrace.$$
> We represent an uncertain prospect as a *lottery* or *probability distribution* over the prize space. For instance, the prospect that Stanford and Cal are equally likely to win Big Game can be written as $p=(1/2,1/2,0)$. Perhaps these probabilities depend on who Stanford starts at quarterback. In that case, there might be two prospects: $p$ or $p'=(5/9,3/9,1/9)$, depending on who starts.

(not sure what I was thinking yesterday evening. It seems like I completely misunderstood the question)

> **Comments:**
> **username_3**: I think they mean lotteries in the MWG sense of uncertain cash flow, not real life lotteries, which are a subset of this.  
> **username_0**: @username_3 you are right. if you can come with a better answer please do  
> **username_3**: @username_0 I think username_1's comment is the appropriate answer.  

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