# Cumulative voting

How would we model cumulative voting (\$100 method) in `brms`?

For example:

Q1: What food do you like out of these five alternatives? A,…,E
Q2: What do you like to drink out of these four alternatives? A,…,D

Each respondent can pick many different strategies, e.g., one could put all \$100 on category no. 1 in Q1, while another might spread them out \$20 each on each category.
{100, 0, 0, 0, 0}
{20, 20, 20, 20, 20}

In Q2 they have \$100 again to spend, and there some might choose to spend \$25 on each category, while some might put \$80 on category 2 and \$20 on category 3.
{25,25,25,25}
{0,80, 20, 0}

In short, in each category, they can place 0-100. The total must be 100 for each question.

I was first thinking a categorical ordered outcome, but is it really that? Compared to a Likert scale, one can pick many categories. In addition, to me, it’s a bit different if two people answer the following on Q1:
{0,10, 20, 30, 50, 0}
{0, 5, 10, 10, 65, 0}

My friend and I discussed this today and he mentioned Dirichlet, and that sounds plausible.

I think we’ll go for modeling it as an ordered logit `Dirichlet` process for now.

Sorry for not responding. Somehow I seem to have overlooked that question. I agree with you that you should be using a dirichlet distribution for this. Hopefully, at some point this year, we will also have that readily available in brms.

No worries - I probably should’ve asked the question in another forum since it’s not `brms` specific per se. As a tip, if anyone will read this later, McElreath plans to add this to Statistical rethinking 2nd Edition, and hopefully, @paul.buerkner will have added it to `brms` by then.

What I don’t understand from your answer is what you mean by “ordered logit” dirichlet process? If we have \$100 to spend and divide the responses by 100, we just get a dirichlet distribution. Where does the ordering come in here?

Hmm, maybe you’re right, e.g., I spend 100 on four items out of seven,
[0, 20, 20, 0, 30, 30, 0] and the items are unordered. But the response distribution is, I would say, ordered in a way: [0,0,0,20,20,30,30].

So we are talking about unordered categorical predictors. In McElreath’s draft, he has an example concerning educational level, but those are ordered (Middle school -> Graduate degree). That’s why I wasn’t sure it was `Dirichlet`.

As long are your seven items have no order, your response (divided by 100) will just be dirichtlet, as you have 7 unordered categories whos “probabilities” sum to 1.

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Just a quick update that dirichlet models are now support in the github version of brms via family `dirichlet()`.

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You’re great - you know that, right? :)

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