Accident and agency: a mixed methods study contrasting luck and interactivity in problem solving

Abstract

Problem solving in a materially rich environment requires interacting with chance. Sixty-four participants were invited to solve 5-letter anagrams presented as movable tiles in conditions that either allowed the participants to move the tiles as they wished or only allowed random shuffling (without rearranging the tiles post shuffling) thus contrasting pure luck with an interactive model. We hypothesised that shuffling would break unhelpful mental sets and introduce beneficial unplanned problem-solving trajectories. However, participants performed significantly worse when shuffling, which suggests luck plays less of a role than has been previously suggested. Granular analysis of seven critical cases revealed arbitrary path dependency across both conditions and moments of missed luck. It also questions current models of non-agentic luck and the ability to separate agent and luck. This research has implications for fostering better problem solving in an uncertain and fluid world.

Keywords:

• Serendipity
• interactivity
• chance discovery
• luck

Acknowledgements

We thank Andrea Marin for her time watching the video corpus alongside us and Paul March, Linden Ball and three anonymous reviewers for helpful comments on a previous version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The cheap necklace problem requires participants to make a complete closed loop (necklace) out of 12 links of chain, with the starting point being 4 smaller, 3-link chains. A cost constraint (2 cents to break a link, and 3 cents to join a link) is imposed. The correct solution involves breaking all three links of one of the 3-link chains, and using the individual links to connect the three remaining 3-link chains together

2 How to distribute 17 animals in four enclosures such that there are an odd number of animals in each enclosure. The solution requires the participants to overlap sets, permitting the double counting of some of the animals.

3 ‘A dealer in antique coins got an offer to buy a beautiful bronze coin. The coin had an emperor’s head on one side and the date 544BC stamped on the other. The dealer examined the coin, but instead of buying it, he called the police. Why?’ Perkins (1981), cited in Fleck and Weisberg (2013)

4 using the RANDINT function in Excel

5 As suggested by a reviewer the idea of “closeness” here requires a lexical realism which may not be sustained on closer analysis. A word either is a word when recognised by a participant or is not and therefore the status of these letter strings is relational to the person observing them. This is also problematic when we are assessing the moments of “missed serendipity” because they are only missed in relation to a problem solver who already knows the answer. We raised similar concerns in Ross and F. Vallée-Tourangeau (2021a). This reveals the complexities of assessing process when the researchers know the answer but the participants do not.