<p>SUPPLEMENTARY MATERIAL [Not intended for publication]</p><p>Unrestricted version </p><p>Restricted version Additional details on the implementation of experiment I In each session, subjects were randomized into four subgroups (S1-S4), each of 25 subjects. Within each subgroup, subjects face two blocks of eight categories. Block 1 contained categories {cities, fruits, car manufacturers, fast food chains, positive numbers, supermarket chains, metals, means of transport} and block 2 contained categories {sports, football players, animals, colours, flowers, items of furniture, drinks, superheroes}. The order in which the different categories are presented is the same across subgroups. Within a session the sets and the order of the blocks is counterbalanced. Subjects in an odd (even) subgroup are matched with a subject from the other odd (even) subgroup. Table A illustrates this procedure.</p><p>TABLE A: ASSIGNMENT OF BLOCKS AND SETS TO SUBJECTS </p><p> subgroup (and number of subjects)</p><p>______</p><p>S1 S2 S3 S4</p><p>(25) (25) (25) (25)</p><p>______</p><p>Block 1 unrestricted 1 – 2 –</p><p>Block 1 restricted – 1 – 2</p><p>Block 2 unrestricted – 2 – 1 Block 2 restricted 2 – 1 – </p><p>______</p><p>Numbers denote the order in which the groups were played (1 = first, 2 = second).</p><p>Additional details on the implementation of experiment II Subjects are randomly allocated to a session of the either unrestricted version or restricted version. The sessions for each version implemented the same procedures. All the subjects in each session are allocated a booklet (B1-B4). Within a session, each booklet is presented in two formats which counterbalance the blocks of eight categories for each stage (allowing subjects to be matched). For each of the eight formats, the order of the rules, categories and labels within and across blocks is always independently randomized. Table B illustrates this procedure.</p><p>TABLE B: ASSIGNMENT OF BLOCKS TO SUBJECTS </p><p>Booklet </p><p>(number of subjects in open/closed for each format)</p><p>______</p><p>B1 B2 B3 B4</p><p>(10/8) (13/16) (13/13) (13/13) </p><p>______</p><p>Format 1</p><p>Naive elicitation 1 3 5 7</p><p>Strategic elicitation 2 4 6 8</p><p>Format 2</p><p>Naive elicitation 2 4 6 8</p><p>Strategic elicitation 1 3 5 7</p><p>______The numbers denote the blocks: 1=categories{sports, football players, positive numbers, supermarket chains, flowers, items of furniture, colours, metals}, 2=categories{cities, fruits, car manufacturers, fast food chain, animals, means of transport, drinks, superheroes}, 3=categories{ sports, football players, positive numbers, car manufacturers, fast food chain, colours, means of transport, drinks}, 4=categories{ cities, fruits, supermarket chains, flowers, items of furniture, animals, metals, superheroes}, 5=categories{fruits, sports, football players, items of furniture, car manufacturers, animals, metals, means of transport}, 6=categories{cities, positive numbers, supermarket chains, flowers, fast food chain, colours, drinks, superheroes}, 7=categories{ sports, football players, positive numbers, car manufacturers, fast food chain, animals, metals, means of transport}, 8=categories{ cities, fruits, supermarket chains, flowers, items of furniture, colours, drinks, superheroes}</p>