experiments in which subjects participated in lotteries. In the first study, lottery tickets were handed out either consecutively from booklets of tickets or randomly ...
Naive conceptions of free will and the deterministic paradox WILLIAM TURNBULL Simon Fraser University
It was predicted that in judging past events people assume that their behavior has been free, but the behavior of others, and the surrounding events, have been determined - the deterministic paradox. These inconsistently deterministic conceptions lead to a number of interesting effects, including a feeling of potential control over chance. Empirical support for the predictions was obtained from two experiments in which subjects participated in lotteries. In the first study, lottery tickets were handed out either consecutively from booklets of tickets or randomly from a drum of loose tickets. The results indicated that the closer a subject's ticket number was to the winning number (1) the closer the subject felt to winning the lottery, and (2) when the ticket was one of a consecutive series the greater was the subject's feeling of potential control over winning. The second experiment manipulated the subjects' perception of the time at which the winning number was determined - either before any, or after all, tickets were handed out. Consistent with the reasoning underlying the deterministic paradox, this variable produced no significant effect on perceptions of control. The results also offered support for the hypothesis that the feeling of closeness to winning is due to a feeling of increased chance of winning that occurs when the winning number is read out: subjects whose ticket number matched the winning number on thefirsttwo digits reported significantly greater feelings of chance of winning than those whose number matched only on thefirstdigit. The relationship between the deterministic paradox and possible worlds, the silly certainty of hindsight, and the illusion of control is discussed.
Most people do not believe in predeterminism. But, consider the following argument: It is true that I ate a sandwich today for lunch. Therefore, yesterday it was the case that today I would eat a sandwich for lunch. Indeed, it was the case since the beginning of time that today I would eat a sandwich for lunch. Therefore, I could not have done anything else but eat a sandwich for lunch today - it was predetermined. In general, I have no freedom, I only do that which was predetermined. Gilbert Ryle (1964) refers to the above dilemma as "It was to be." Ryle removes the reader from the horns of the dilemma. What is more interesting psychologically, however, is that most people feel its force. In analyzing the dilemma, a certain conception of free will emerges. The basis of the dilemma is the assumption that if an event, X, occurs at time t^, then it was true at time t0 (where t0 is any time before fi) that X would occur at time r^ Stated differently, the assumption is that, given that it is true that X occurs at tt, then it had to be the case This article is based upon dissertation research. I would like to thank the members of the dissertation committee for their support: Sam Fillenbaum, Chet Insko, John Schopler, John Thibaut, and Steve Worchel. Thanks are also due to Dennis Krebs and Ray Koopman. Correspondence should be addressed to William Turnbull, Department of Psychology, Simon Fraser University, Burnaby, British Columbia, Canada, V5A 1S6. CANAD. J. BEHAV. SCI./REV. CANAD. SCI. COMP. 13(1), 1981
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at t0 that X would occur at the later time tx. And since it had to be the case at t0 that X must occur at tx, then nothing else could have occurred at t\. It has already been stated that most people find the notion of predeterminism unacceptable. It has also been stated that most people find the reasoning underlying "It was to be" equally acceptable. The dilemma arises from holding both beliefs. It will be argued in this paper that when individuals think about or interpret past events they hold both beliefs, but they do so in a way that does not create a dilemma. A specific example may help clarify the issue. A certain Father Raimondo Salvaggio of Rome, Italy, was standing in line to purchase a lottery ticket when he "... courteously allowed another man to step ahead of him at the lottery counter. The man's 800 ticket - the one Father Salvaggio would have bought - was good for $192,000. So much for good and evil. To say nothing of courtesy" (Sports Illustrated, February 8, 1971, page 41). The assumption that underlies the poignancy of the incident is that the winning ticket would have been, and should have been, Father Salvaggio's. The assumption appears rational, and would naturally be endorsed by most of us. Let's examine it. In order to conclude that the winning ticket would have been Father Salvaggio's we must assume that the ticket that subsequently won the lottery was the winning ticket at the time Father Salvaggio stood in line even though it had not at that time been picked as the winning ticket. That is, the assumption is that the ticket that won the lottery at a later point in time was determined as the winner (had to be the winner) at an earlier point in time. This aspect of the world was fixed and determined. The second assumption is that Father Salvaggio could have acted differently, and thus won the lottery. But, if events are predetermined, why wasn't Father Salvaggio's behavior (allowing a person to step in front of him) predetermined? Either we must account for both events by the same principle or have a law that some events are predetermined and others are not. This is the logical analysis, but what of the psychological reasoning? The example of Father Salvaggio suggests that the average person conceives of his own past behavior (or the behavior of those he identifies with) as being free while conceiving of the past behavior of others, including natural events, as rooted in a matrix of determinism. We refer to thinking about the past in this manner as reasoning in accordance with the deterministic paradox. In this paper, we examine the way in which reasoning in terms of the deterministic paradox can lead to the perception of potential personal control over purely chance determined events. The present studies are concerned with individuals' reactions to a lottery in which they had participated. The numerical closeness of lottery ticket numbers to the winning number was systematically varied. It was hypothesized that the numerically closer one's ticket number to the winning number, the closer to winning one feels - the Closeness Effect. Numerical order is identified as critical for the Closeness Effect. However, numerical order is confounded both with number of similar digits and physical order. In general, numerically close numbers
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share more digits than numerically remote numbers; and lottery tickets are placed in booklets according to numerical order such that numerically adjacent tickets are also physically adjacent. Results from a study by Turnbull and Schopler (Note 1) contradict the digit similarity interpretation. A lottery participant was rated as significantly closer to winning the lottery when his ticket number was numerically close to the winning number than when it was either numerically remote and dissimilar or numerically remote but identical on five or six digits. Numerical and physical order were unconfounded in one condition of the present studies by randomizing the tickets before they were handed out. The Closeness Effect was predicted for this condition also since numerical order remained intact. The contention that people fall into the deterministic paradox when thinking about their past was examined by assessing participants' feelings of control about their outcome. According to the deterministic paradox, participants believe that the winning number was fixed and determined, but can imagine that they could have behaved differently, thereby obtaining a different number - in particular, the winning number. It was predicted that the easier it was to imagine what one might have done in order to get the winning number, the greater one's feeling of potential control. If tickets are handed out consecutively (i.e., numerical and physical order are in a one-to-one correspondence), then it is easy to imagine what one might have done. For example, if the ticket received were two countable numbers preceding the winning number or one following, one could have waited two turns, or arrived one person earlier. Thus, the closer one's number to the winning number, the easier it is to imagine having acted differently, and therefore the greater one's feelings of control. However, if tickets are randomized, thereby destroying the numerical/physical order correspondence, no matter what number one received it should be very difficult to imagine what else one might have done to get the winning number. It was therefore predicted (1) that participants who received a ticket from a booklet of consecutively-numbered tickets would perceive greater potential control than those who received a ticket from a randomized collection; and (2) that, within the consecutively-numbered condition only, the numerically closer one's number to the winning number, the greater perceived control.
EXPERIMENT I METHOD Subjects Subjects were 582 male and female introductory psychology students from the University of North Carolina who participated in the experiment in partial fulfillment of a course requirement. Procedure Subjects were run in groups ranging in size between 42 and 49. On arriving at the experimental room, subjects received a lottery ticket, either from a booklet (Ordered condition) or randomly from a box of
TABLE 1 Four-factor analyses of variance on each of the dependent variables Closeness Source Numerical Distance (N) Before/After (B) Ordered/Random (0) Groups within Ordered/Random (G(0)) BN ON OB OBN *p < .05. **/>
