Asking better questions to build a decision model

How would you explain what makes a car acceptable: by assigning numerical weights to cost, performance and safety, or by judging carefully chosen examples? Eda Ersek Uyanık’s doctoral thesis explores the second approach, developing algorithms that select questions to uncover a decision-maker’s sorting rules.

The work was posted as an arXiv preprint on 9 November 2026, but it is not newly completed research: the source identifies it as a thesis defended at the University of Mons in Belgium in July 2023. Its evidence consists principally of mathematical analysis and exhaustive computer simulations, not trials showing that people make better decisions with the software.

Two ingredients behind an acceptable option

The thesis studies a basic version of the Non-Compensatory Sorting model, or NCS, with two categories and no vetoes. A veto would allow an exceptionally poor result on one criterion to block acceptance regardless of other strengths.

The basic model needs two ingredients. First, a boundary level on each criterion separates satisfactory from unsatisfactory performance. Together, these levels form a boundary profile. Second, the model specifies which combinations of satisfactory criteria are enough for overall acceptance. These combinations are called sufficient coalitions.

Here, “non-compensatory” has a precise meaning. Once performance on a criterion is satisfactory, improving it further cannot rescue an option whose combination of satisfactory criteria is insufficient. The model records which requirements are met, rather than how far they are exceeded.

A sufficient coalition remains sufficient when more criteria become satisfactory. This consistency rule saves questions: an accepted combination establishes that every larger combination is also acceptable; a rejected combination establishes that every smaller one is insufficient.

Choosing the next question

To test a coalition, the analyst presents a hypothetical option with clearly satisfactory performance on its criteria and clearly unsatisfactory performance elsewhere. The decision-maker assigns that option to a category. This avoids asking for weights whose meaning may be difficult to understand or depend on the chosen model.

One algorithm, DFS3, explores a graph of criterion combinations and asks questions near the middle of its branches. Answers establish the status of other combinations through the consistency rule. Its implementation can also use additional information about the relative importance of criteria or coalitions, provided that information supports the required logical deductions.

A second approach adapts an existing result by Hansel concerning monotone Boolean functions—yes-or-no rules that cannot switch from yes to no when inputs improve. The thesis develops a modified graph-search construction of Hansel’s chains and implements a questioning procedure called DFSHansel.

DFSHansel minimizes the maximum number of coalition questions that might be needed. With four criteria, its worst-case requirement is 10 questions; DFS3 sometimes needs 11. That guarantee does not mean DFSHansel wins for every individual rule.

The researcher also calculates strategies that minimize the average question count for up to four criteria, assuming every possible coalition rule is equally likely. For four criteria, the reported optimum is about 7.65 questions, compared with about 7.90 for DFSHansel and 8.09 for DFS3. These figures concern identifying coalitions, not the entire interview.

Boundary levels require a separate procedure. Holding other criteria at suitable fixed levels, the analyst varies one criterion and asks whether the resulting option is acceptable. Repeatedly halving the remaining interval locates its boundary to a chosen precision.

Why weights cannot express every rule

The thesis also investigates MR-Sort, a restricted NCS model in which each criterion has a weight and a coalition succeeds when its weights reach a threshold.

Consider the thesis’s education example: a student must achieve a satisfactory mark in at least one language subject and at least one science subject. Two language successes alone are insufficient, as are two science successes alone. No single set of additive criterion weights and one threshold can reproduce all these requirements.

Using exhaustive enumeration through six criteria and linear-programming tests, the study measures this representational gap. Among all 7,828,354 coalition-rule families for six criteria, only 3.12% can be represented by additive weights and a threshold. A further 95.02% require pairwise interaction terms, and 1.86% require three-way terms. These are proportions of mathematical possibilities, not estimates of how commonly people hold such preferences.

The interview remains the hard part

The rigorous procedures assume reliable, consistent answers and suitable hypothetical combinations of criterion values. They minimize question counts, not psychological difficulty, and are not designed to detect inconsistent answers automatically.

The thesis therefore discusses combining questioning with methods that infer models from examples, retaining uncertainty about boundaries, and checking whether NCS actually fits someone’s judgments. Vetoes, additional categories and criterion hierarchies are discussed as extensions. The practical contribution is a disciplined way to construct questions—not proof that a short mathematical interview captures real preferences without further validation.