The Linda problem.
Read four short scenarios and, in each one, choose which of two options is more probable.
Original study
- Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90(4), 293–315. Source
- Hertwig, R., & Gigerenzer, G. (1999). The 'conjunction fallacy' revisited: How intelligent inferences look like reasoning errors. Journal of Behavioral Decision Making, 12(4), 275–305. Source
- Mellers, B., Hertwig, R., & Kahneman, D. (2001). Do frequency representations eliminate conjunction effects? An exercise in adversarial collaboration. Psychological Science, 12(4), 269–275. Source
- Charness, G., Karni, E., & Levin, D. (2010). On the conjunction fallacy in probability judgment: New experimental evidence regarding Linda. Games and Economic Behavior, 68(2), 551–556. Source
- Chandrashekar, S. P., Cheng, Y. H., Fong, C. L., Leung, Y. C., Wong, Y. T., Cheng, B. L., & Feldman, G. (2021). Frequency estimation and semantic ambiguity do not eliminate conjunction bias, when it occurs: Replication and extension of Mellers, Hertwig, and Kahneman (2001). Meta-Psychology, 5. Source
- Fiedler, K. (1988). The dependence of the conjunction fallacy on subtle linguistic factors. Psychological Research, 50(2), 123–129. Source
Our adaptation
A four-scenario adaptation of Tversky and Kahneman's (1983) conjunction fallacy problems. In the Linda and Bill scenarios a personality description, and in the health screening scenario a cause-effect link, makes the conjunction attractive; in each, the more probable of two options (single event or conjunction) is chosen and option order is randomized. The last round asks the same question in frequency format ('how many out of 100 people?'). Before answering, participants are asked whether they had seen the problem before.
Differences from the original study
- The original was a single problem; here four problems are asked in one session and learning effects are possible.
- There is no incentive; Charness et al. (2010) found that incentives reduce the fallacy.
- The texts were translated into Turkish for the Turkish interface (the name Linda is kept).
Measured variables
The columns of the open data file. List fields are expanded into numbered columns (for example rt_60, est_3); JSON columns contain only numbers and fixed stimulus names.
| Column | Type | Description |
|---|---|---|
pick | single | conj | Round 1 (Linda): chosen option (single = single event, follows the rule; conj = conjunction, fallacy). |
order | sc | cs | Round 1 option order (sc = single first, cs = conjunction first). |
bill | single | conj | Round 2 (Bill): chosen option. |
health | single | conj | Round 3 (health screening): chosen option. |
freq_single | integer | Round 4 (frequency format): estimate of 'how many out of 100' for the single event. |
freq_conj | integer | Round 4: estimate of 'how many out of 100' for the conjunction (the rule is broken if it exceeds the single event). |
order_bill | sc | cs | Round 2 option order. |
order_health | sc | cs | Round 3 option order. |
Columns present in every file (14)
row_id | string | Row code. Regenerated at random in every release; it does not identify a person and cannot be matched across releases or experiments. |
experiment | string | Short name of the experiment (URL slug). |
experiment_version | integer | Version of the answer format. For experiments whose format changed, only the current format is published. |
date | YYYY-MM-DD | YYYY-Www | YYYY-MM | Day the answer was given (Istanbul time). If fewer than 5 answers share the same day, language and device, it is coarsened to the ISO week, and to the month if that is still too few. |
date_precision | day | week | month | Precision of the date column. |
lang | tr | en | (boş) | Interface language. Language recording started in the first week of October 2026; for earlier answers it is known only in experiments whose stimuli depend on the language, and empty otherwise. |
device | desktop | mobile | tablet | (boş) | Device class reported by the browser (class only; browser details are neither stored here nor published). |
source | site | embed | Where the answer came from: the balabs site or the experiment embedded on another site. The embedding site is not published. |
mode | free | daily | challenge | race | session | (boş) | Play mode in scored experiments: free play, daily round, challenge, race room, experiment session. Empty for unscored experiments and for older answers that did not store it. |
color_vision | normal | rg | by | contrast | (boş) | In color-based experiments, the color vision mode the participant chose: normal, red-green, blue-yellow or high contrast. Stimuli are generated along different axes per mode, so compare within a mode. Empty for other experiments. |
first_play | 1 | Every row is a participant’s first play of this experiment (always 1). Replays are stored only as leaderboard scores and are not part of the open data. |
seen_before | yes | no | unsure | (boş) | Participant’s own report of whether they had seen this experiment or its known answer before (in experiments that ask). |
duration_s | number | Time from the start of the experiment to submitting the answer, in seconds (measured in the browser, 0.1 s). |
play_score | number | Leaderboard score of the first play (scored experiments; defined on the method card). Empty for unscored experiments. |
Exclusion criteria
The server requires the round-1 choice (single | conj) and re-checks the frequency estimates as whole numbers from 0 to 100. We recommend reporting participants who say they had seen the problem before (seen_before) separately.
- Only each participant's first answer to this experiment; replays are not included.
- Simulated rows, bots, banned and sample accounts are not included.
- Answers before 3 October 2026 are not included (the first day the open data notice was live).
Scoring
Leaderboard score: number of rounds following the rule (0–4): choosing the single event for Linda, Bill and health screening, and not estimating the conjunction above the single event in the frequency round. Higher is better.
Leaderboard measure: correct (higher is better). The play_score column in the open data is this score for the first play.
Version notes
- October 2026
This experiment started storing the play mode (free, daily, challenge, race, session) with the answer; the mode column is empty for earlier answers.
- October 2026
The interface language (lang) started being stored with each answer; for earlier answers it is known only in experiments whose stimuli depend on the language, and empty otherwise.