Make 22 choices from budget lines, then test whether they are consistent with maximizing a stable preference. This is the Weak Axiom of Revealed Preference (WARP), checked on your own choices.
Each gray line is one round; each dot is what you chose. Rounds involved in a WARP violation are red. Select a violation to see why.
Consistency index (CCEI) for 500 simulated people who clicked at random on your 22 lines. 1.0 means perfectly consistent.
If you choose bundle A when bundle B was also affordable, you have revealed that you prefer A to B, or at least like it as much. WARP says you should then never choose B when A is affordable.
Drag the round handles to choose a bundle on each line, and the square handles on the axes to move the lines. Shaded areas show what each budget can afford.
Violations need crossing lines. If one budget lies inside the other, the bundle from the smaller budget is always affordable on the larger one, but never the reverse, so no contradiction is possible.
Consistency in general is tested with GARP, which also catches longer cycles: A over B, B over C, and C over A. With only two goods, every such cycle also contains a direct pairwise contradiction, so WARP and GARP give the same verdict (Rose, 1958). With three or more goods they come apart, and choices can pass WARP yet violate GARP.
That is why your results list only pairs of rounds. The CCEI below is computed with GARP, the standard in the literature.
Afriat's critical cost efficiency index asks: by how much must every budget shrink before the contradictions disappear? Shrinking a budget makes fewer alternatives count as "affordable", so fewer preferences are revealed. A CCEI of 0.95 means you wasted at most 5% of your budget by choosing inconsistently.
Dashed lines are the shrunken budgets (each multiplied by e). A bundle counts as affordable on a round only if it lies under that round's dashed line. Lower e until no violations are left: the highest e at which that happens is the CCEI.
Damage to ventromedial prefrontal cortex. Patients with vmPFC lesions made more inconsistent choices than control patients in preference tasks, suggesting this region supports coherent valuation. Camille, Griffiths, Vo, Fellows & Kable (2011), Journal of Neuroscience.
Noisy value signals. With this budget-line task in the fMRI scanner, the degree of inconsistency was linked to activity in value-related regions, consistent with choices driven by a noisy neural value computation. Kurtz-David, Persitz, Webb & Levy (2019), Nature Communications.
The task itself. Choices over two risky accounts on randomly drawn budget lines, scored with GARP and the CCEI. Choi, Fisman, Gale & Kariv (2007), American Economic Review.
Discussion question: if most people score above 0.9, is that evidence for utility maximization, or does the remaining inconsistency tell us more about how the brain computes value?