# Difference vs. Ratio of evidence in sequential sampling models

In sequential sampling models - for instance Ratcliff and Smith, (2006) - participants' responses in a binary choice experiment are modelled by a particle, which moves up or down towards the boundaries for selecting each response over time according to the evidence in favour of each, or, analogously, their expected utility (Busemeyer & Townsend, 1993), in a way that looks something like this: My question is if anyone knows, and preferably can provide a reference for, whether in such a model responses are best predicted by

• the difference in the evidence for/expected utility of each response (i.e. $P(Response\ A) = Evidence\ for\ A - Evidence\ for\ B$) or
• the ratio of evidence/expected utility (i.e. $P(Response\ A) = \frac{Evidence\ for\ A}{Evidence\ for\ B}$)

My intuition is that it's the ratio between the two responses, rather than the absolute difference, which should best predict responses, but I can't find a reference for this, and I'm sure this question has been answered somewhere before.

Has anyone any ideas here?

• Partial credit (+1): the reference is a good one (thanks), but as I understand it, it suggests the ratio to be best predictor in principle: "The decision requires the construction of a DV [decision variable] from e [the evidence]. For binary decisions, the DV is typically related to the ratio of the likelihoods of $h_1$ and $h_2$ given e: $l_{12}(e) ≡ P(e | h_1)/P(e | h_2)$". – Eoin Nov 16 '15 at 14:57
• I think what you say about the case of $Something/0$ requires that participants begin each trial with a prior value $0$ for each option, which isn't true - unbiased participants should start with a prior of $.5$ on each option, and adjust this belief in response to new evidence. – Eoin Nov 16 '15 at 15:01