Note

Link to an example general dataset that can be analysed for stochastic choice consistency as described later on this page.

Stochastic Consistency Criteria for General Datasets

For general datasets where the same menus appear more than once, Prest can compute, view and export the total number of violations of each of the axioms/criteria of stochastic choice consistency listed below, for every subject in the dataset.

In the statements that follow, for a given menu \(A\) in general dataset \(\mathcal{D}\), and any alternative \(a\) in that menu, \(Pr(a,A)\) denotes the choice frequency or choice probability of \(a\) at the different presentations of menu \(A\) for some agent in \(\mathcal{D}\).

Weak Stochastic Transitivity

For all \(x,y,z\in X\), \(Pr(x,\{x,y\})\geq \frac{1}{2}\) and \(Pr(y,\{y,z\})\geq \frac{1}{2}\) implies \(Pr(x,\{x,z\})\geq \frac{1}{2}\).

Moderate Stochastic Transitivity

For all \(x,y,z\in X\), \(Pr(x,\{x,y\})\geq \frac{1}{2}\) and \(Pr(y,\{y,z\})\geq \frac{1}{2}\) implies \(Pr(x,\{x,z\})\geq \min\{Pr(x,\{x,y\}),Pr(y,\{y,z\})\}\).

Strong Stochastic Transitivity

For all \(x,y,z\in X\), \(Pr(x,\{x,y\})\geq \frac{1}{2}\) and \(Pr(y,\{y,z\})\geq \frac{1}{2}\) implies \(Pr(x,\{x,z\})\geq \max\{Pr(x,\{x,y\}),Pr(y,\{y,z\})\}\).

Regularity

For all menus \(A\), \(B\) in \(\mathcal{D}\) such that \(A\supset B\), and for all \(x\) in \(A\), \(Pr(x,A)\leq Pr(x,B\}\).

Tip

To use the stochastic-consistency feature: right-click on the dataset of interest [e.g. “DatasetX.csv”] in the workspace and select “Analysis -> Stochastic consistency analysis”.

To view the stochastic-consistency output: right-click on the Prest-generated dataset [“DatasetX.csv (stochastic consistency)”] in the workspace and then click on “View”.

To export the stochastic-consistency output (in .xslx or .csv format): right-click on the Prest-generated dataset [“DatasetX.csv (stochastic consistency)”] in the workspace, and click on “Export” and “Summary…”.