Humans are in general poor at making judgments that adhere to the logical principles of probability theory. One demonstration of this is termed the “conjunction fallacy”: judging a conjunction (A&B) as being more probable than its constituent (A). Systematic commitment of the conjunction fallacy has been shown in numerous studies on probability judgments. Different actions to remedy the fallacy have been suggested. According to the nested-sets hypothesis, when the nested-set structure of a problem becomes clear (i.e. the relation between categories and subcategories), then the conjunction fallacy is remedied. However, previous demonstrations of this remediation have provided very explicit task-related information and it can be questioned whether it is trivial that such information leads to more correct judgments. The primary aim of this study was to test the nested- sets hypothesis in two different formats of a probability judgment task, by more subtly hinting about the nested-set structure. Twenty-nine participants were randomly divided into two groups, one Probability condition and one Informed probability condition, where participants in the latter condition were provided with the hint. The second aim was to investigate whether the Informed probability condition was performed more slowly, potentially due to the time-cost of more elaborated judgments. The results show that a subtle hint about the nested-set structure was able to remedy the conjunction fallacy in a forced-choice probability judgment task but not statistically reliably in a probability estimation task. No response-time differences were observed between the conditions. The results support the nested-sets hypothesis and imply that even a subtle reasoning hint clarifying the relation between categories and subcategories might remedy one of the most robust probability judgment fallacies. / Människor är i allmänhet dåliga på att göra bedömningar som följer principer för sannolikhetsteori. En indikation på det är ”konjunktionsfelet”: att bedöma en konjunktion (A&B) som mer sannolik än sin konstituent (A). Konjunktionsfelet har påvisats i flera studier på sannolikhetsbedömningar. Olika sätt att avhjälpa felet har föreslagits. Enligt nested-set hypotesen föreslås att när nested-set strukturen av ett problem blir tydlig (dvs. relationen mellan kategorier och subkategorier), minskas benägenheten att begå konjunktionsfelet. Däremot har tidigare demonstrationer av den här minskningen angett väldigt explicit uppgifts-relaterad information och det kan ifrågasättas om det är trivialt att sådan information leder till mer korrekta bedömningar. Studiens primära syfte var att testa nested-set hypotesen i två olika sannolikhetsbedömningsformat, genom att subtilt antyda om nested-set strukturen. Tjugonio deltagare delades slumpmässigt in i två grupper, en Sannolikhetsbetingelse och en Informerad sannolikhetsbetingelse, där den senare betingelsen fick den extra informationen. Det andra syftet var att undersöka om Informerad sannolikhetsbetingelsen skulle utföras långsammare, potentiellt på grund av tids-kostnaden av mer elaborerade bedömningar. Resultatet visar att en subtil antydan om nested-set strukturen minskade konjunktionsfelet i en fler-vals uppgift på sannolikhetsbedömningar men inte statistiskt pålitligt i en sannolikhetsestimeringsuppgift. Inga responstidsskillnader hittades mellan betingelserna. Resultat stödjer nested-set hypotesen och antyder att även en subtil antydan som klargör relationen mellan kategorier och underkategorier kan åtgärda ett av de mest robusta tankefel som observerats vid sannolikhetsbedömningar.

Studien undersökte konjunktionsfelslutet och hur det påverkas av förvåning och en konjunktions komponentlängd. En konjunktion (A&B) kan enligt sannolikhetslärans konjunktionsregler endast vara mindre eller lika sannolik som någon av dess komponenter (A eller B). Bryts denna regel begås ett konjunktionsfelslut. 227 deltagare (142 män och 86 kvinnor) randomiserades till 2 olika betingelser och fick utifrån olika långa konjunktioner av fotbollsrelaterade matchresultat antingen bedöma resultatens sannolikhet eller hur förvånade de blev av utfallet. Konjunktionerna var varierande långa och innehöll upp till 3 matchresultat som var utformade för att upplevas som mycket sannolika samt 1 matchresultat som utformats för att upplevas som mycket osannolik. Inga signifikanta resultat erhölls för att antalet konjunktionsfelslut förändras tillsammans med konjunktionens komponentlängd. Ju fler sannolika komponenter en konjunktion hade desto sannolikare (η2part=0,145) och mindre förvånande (η2part=0,336) bedömdes den däremot vara. Korrelationen mellan sannolikhet och upplevd förvåning utifrån varje konjunktions medelvärden var r=-0.985. Resultatet tyder på antalen konjunktionsfelslut inte påverkas av komponentlängden men däremot att konjunktionens utformning kan influera bedömningen av olika valalternativ samt att förvåning har ett mycket starkt samband med sannolikhetsbedömningar.

<p>According to the heuristics and biases approach, the representativeness heuristic (RH) is one of the heuristics available for assessing subjective probabilities (A. Tversky & D. Kahneman, 1974). A subjective probability assessed by the RH is determined by how representative the target object is of the target category. Several aspects of the RH are argued to cause systematic biases, for example: (<i>i</i>) When the RH is used, the category is represented by one single prototypical exemplar. This feature is argued to cause biases such as misperception of chance and insensitivity to sample size. (<i>ii</i>) The RH assesses the inverse rather than the conditional probability. This feature is argued to cause biases such as the conjunction fallacy and base-rate neglect.</p><p>The present thesis focuses on the cognitive aspects of the RH. Three studies were conducted. Overall, data indicated that the RH does not play a major role when subjective probabilities are assessed. Study I indicated that subjective probabilities are not typically determined by how representative the target object is of the target category. Study II indicated that the category is not represented by one single prototypical exemplar when subjective probabilities are assessed. Study III indicated that conjunction fallacies are not caused by the RH. </p><p>The results presented in Studies I-III cast serious doubts on the claim that subjective probabilities are routinely assessed using the RH. Rather, Studies I-II suggested that subjective probabilities are based on exemplar memory and Study III suggested that the conjunction fallacy is caused by people combining component probabilities in a an inappropriate way. In the General Discussion, it is suggested that people use a weighted average rule when combining component probabilities into conjunction probabilities. A simulation showing the ecological relevance of the weighted average rule is presented.</p>

According to the heuristics and biases approach, the representativeness heuristic (RH) is one of the heuristics available for assessing subjective probabilities (A. Tversky &amp; D. Kahneman, 1974). A subjective probability assessed by the RH is determined by how representative the target object is of the target category. Several aspects of the RH are argued to cause systematic biases, for example: (i) When the RH is used, the category is represented by one single prototypical exemplar. This feature is argued to cause biases such as misperception of chance and insensitivity to sample size. (ii) The RH assesses the inverse rather than the conditional probability. This feature is argued to cause biases such as the conjunction fallacy and base-rate neglect. The present thesis focuses on the cognitive aspects of the RH. Three studies were conducted. Overall, data indicated that the RH does not play a major role when subjective probabilities are assessed. Study I indicated that subjective probabilities are not typically determined by how representative the target object is of the target category. Study II indicated that the category is not represented by one single prototypical exemplar when subjective probabilities are assessed. Study III indicated that conjunction fallacies are not caused by the RH. The results presented in Studies I-III cast serious doubts on the claim that subjective probabilities are routinely assessed using the RH. Rather, Studies I-II suggested that subjective probabilities are based on exemplar memory and Study III suggested that the conjunction fallacy is caused by people combining component probabilities in a an inappropriate way. In the General Discussion, it is suggested that people use a weighted average rule when combining component probabilities into conjunction probabilities. A simulation showing the ecological relevance of the weighted average rule is presented.

According to the conjunction rule of probability theory, a conjunction of events cannot be more probable than either conjunct. However, participants often violate this rule in experimental settings, thus committing the conjunction fallacy. Why do participants commit this fallacy? One hypothesis suggests that participants interpret a task-critical statement designating the event A as designating the event A&amp;notB. If so, participants do not commit the conjunction fallacy. Another hypothesis suggests that participants fail to take task-relevant relations of set inclusion into account when judging probabilities. Both hypotheses were tested in an experiment utilizing a between-subjects design with 145 participants. The results, analyzed using Bayes factors, provide evidence for the null hypothesis in both cases, thus suggesting that neither hypothesis explains the fallacy. However, the unexpectedly low prevalence of the fallacy in the baseline group may have masked the true effects of the manipulations.

Heuristic estimates of probabilities may be an obstacle to decision making within High Reliability Organizations. Accident reports have found that two from each other separate phenomenon, Blame Culture and Type 1 processing constitutes a particularily serious threat to decision making. The present study (N = 70) investigated if a perceived risk of negative feedback and cognitive load would lead to more heuristic estimates on the Conjunction Fallacy. Three experiment conditions were included in the study: Negative feedback, cognitive load and control. The results were non-significant for both negative feedback and cognitive load. Furthermore, the estimated negative affect was higher when violations to the Conjunction Rule was made. Previous studies showing that high scores on the Cognitive Reflection Test (CRT) indicate less sensitivity to conjunction fallacies, were replicated. The present study concluded that the CRT may be a strong predictor of the Conjunction Fallacy.

Humans repeatedly commit the so called “conjunction fallacy”, erroneously judging the probability of two events occurring together as higher than the probability of one of the events. Certain hints have been shown to mitigate this tendency. The present thesis investigated the relations between three psychological factors and performance on conjunction tasks after reading such a hint. The factors represent the understanding of probability and statistics (statistical numeracy), the ability to resist intuitive but incorrect conclusions (cognitive reflection), and the willingness to engage in, and enjoyment of, analytical thinking (need-for-cognition). Participants (n = 50) answered 30 short conjunction tasks and three psychological scales. A bimodal response distribution motivated dichotomization of performance scores. Need-for-cognition was significantly, positively correlated with performance, while numeracy and cognitive reflection were not. The results suggest that the willingness to engage in, and enjoyment of, analytical thinking plays an important role for the capacity to avoid the conjunction fallacy after taking a hint. The hint further seems to neutralize differences in performance otherwise predicted by statistical numeracy and cognitive reflection. / Människor begår ofta det så kallade ”konjuktionsfelslutet”, genom att felaktigt bedöma sannolikheten för sammanträffandet av två händelser som större än sannolikheten för en av händelserna. Vissa typer av ledtrådar har visat sig mildra denna tendens. Denna uppsats undersökte relationerna mellan tre psykologiska faktorer och prestation på konjunktionsuppgifter efter att ha läst en sådan ledtråd. Faktorerna motsvarade förståelsen för sannolikhet och statistik (statistisk räknefärdighet, eng., statistical numeracy), förmågan att motstå intuitiva men felaktiga slutsatser, (kognitiv reflektion, eng., cognitive reflection), samt viljan och lusten till analytiskt tänkande (behov-av-tänkande, eng., need-for-cognition). Deltagare (n = 50) besvarade 30 korta konjunktionsuppgifter och tre psykologiska mätskalor. En bimodal svarsfördelning motiverade dikotomisering av resultaten. Behov-av-tänkande var signifikant, positivt korrelerat med prestation, vilket varken räknefärdighet eller kognitiv reflektion var. Resultaten tyder på att viljan och lusten till analytiskt tänkande spelar en viktig roll i förmågan att undvika konjunktionsfelslutet efter att ha fått en ledtråd. Ledtråden verkar också neutralisera skillnader i prestation som annars uppstår på grund av räknefärdighet och kognitiv reflektion.

Previous research on human judgment and decision making has demonstrated systematic and predictable biases of judgment in experimental settings. One example of this is the tendency to intuitively violate the conjunction rule - a simple rule of probability. This was well illustrated in the famous Linda-problem. (Tversky &amp; Kahneman, 1983). According to the dual-process theory of reasoning, (Kahneman, 2011) reasoning fallacies such as the conjunction fallacy occurs when people fail to use analytic reasoning and instead overly rely on their intuition. The dual process theory proposes that cognitive processes underlying our intuitive impulses and our conscious reasoning constitutes two different modes in the mind –system 1 and system 2- and that the intuitive system 1 are not able to compute probabilities. Furthermore, it is assumed that processes that are labeled system 1 are fast whereas system 2 are thought to be slow. We tested these time course assumptions of dual process theory in a within-subject design by comparing response time latencies between conjunction fallacy judgments and accurate probability judgments. The results showed that inducing accurate responding did not result in delayed response latency. This indicates that making accurate probability judgments does not require more processing time which goes against what would be expected by the dual-process framework. / Tidigare forskning om mänskligt beslutsfattande och bedömningar har i experiment påvisat systematiska och förutsägbara bias. Ett exempel på detta är tendensen att intuitivt gå emot konjuktionsregeln- en enkel regel gällande sannolikhet. Detta illustrerades väl i det berömda Linda- problemet (Tversky &amp; Kahneman, 1983). Enligt två-systemsteorin (Kahneman, 2011) om problemlösning, uppstår bedömningsfel såsom konjuktionsfelet när människor inte använder sig av analytiskt tänkande och istället förlitar sig för mycket på sin intuition. Två-systemsteorin menar att de kognitiva processer som ligger till grund för våra intuitiva impulser och vårt medvetna resonerande utgör två olika aktörer i vårt tänkande- system 1 och system 2- och att det intuitiva system 1 inte kan beräkna sannolikheter. Processer som betecknas som tillhörande system 1 är enligt två-systemsteorin snabba medan system 2 föreställs vara ett långsamt system. I denna studie testades antagandet om tidsåtgång för de två systemen i en inomgruppsdesign genom att jämföra responstider mellan bedömningar där konjunktionsfelet begåtts och bedömningar där det inte begåtts. Resultaten visar att korrekta sannolikhetsbedömningar inte resulterar i långsammare responstider. Detta indikerar att det inte tycks vara mer tidskrävande att göra riktiga sannolikhetsbedömningar, vilket motsäger två-systemsteorins antagande om snabbt och långsamt processande.