The epistemic virtues of consistency

The lottery paradox has been discussed widely. The standard solution to the lottery paradox is that a ticket holder is justified in believing each ticket will lose but the ticket holder is also justified in believing not all of the tickets will lose. If the standard solution is true, then we get the paradoxical result that it is possible for a person to have a justified set of beliefs that she knows is inconsistent. In this paper, I argue that the best solution to the paradox is that a ticket holder is not justified in believing any of the tickets are losers. My solution avoids the paradoxical result of the standard solution. The solution I defend has been hastily rejected by other philosophers because it appears to lead to skepticism. I defend my solution from the threat of skepticism and give two arguments in favor of my conclusion that the ticket holder in the original lottery case is not justified in believing that his ticket will lose.     

THE LOTTERY PARADOX AND OUR EPISTEMIC GOAL

Abstract: Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no valid reason not to give preference to the derived accounts over the accounts from which they come.     

Another look at why people are reluctant to exchange lottery tickets

People are reluctant to exchange lottery tickets, a result that previous investigators have attributed to anticipated regret. The authors suggest that people's subjective likelihood judgments also make them disinclined to switch. Four studies examined likelihood judgments with respect to exchanged and retained lottery tickets and found that (a) exchanged tickets are judged more likely to win a lottery than are retained tickets and (b) exchanged tickets are judged more likely to win the more aversive it would be if the ticket did win. The authors provide evidence that this effect occurs because the act of imagining an exchanged ticket winning the lottery increases the belief that such an event is likely to occur.     

The role of affect in the WTA/WTP disparity

Four studies demonstrated robust within‐ and between‐subject differences in willingness‐to‐pay (WTP) and willingness‐to‐accept (WTA) measures of the value of lottery tickets. Buyers and sellers attended to different numerical cues and interpreted the same numbers differently when setting these two kinds of monetary values. Affective influences appeared to guide the valuation process. Buyers with stronger positive feelings about owning a ticket were willing to pay more for a ticket; sellers with stronger negative feelings about no longer having a ticket required a greater minimum payment in exchange for their ticket. In addition, the WTA/WTP disparity tended to be greater for more affectively‐laden lottery tickets. The results suggest that WTA and WTP prices are constructed using salient numerical cues and affective feelings. Copyright © 2003 John Wiley & Sons, Ltd.     

The Reinforcing Value of Lottery Tickets,and the Synergetic Effect of Distinct Reinforcements

We present two experiments that explore the reinforcing value of lottery tickets. Participants are faced with a repeated choice task between a safe alternative and a risky prospect that provides a chance to win a lottery ticket to be played at the end of the study. Study 1 considers situations in which the risky option leads to a slightly higher expected value than the safe alternative. It shows that the risk‐taking rate increases with the probability to win the lottery ticket, but it is below 50% even when this probability is high. Study 2 shows limited sensitivity to the expected value of the risky prospect. The results can be explained with the assumption that participants rely on small samples of past experiences, and that their reaction to lottery tickets reflects large variability. The relationship between the current results and previous research on the synergetic effect of distinct reinforcements and the “pat on the back paradox” is discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Consequences of regret aversion in real life: The case of the Dutch postcode lottery

Although ample research has shown that decisions may cause regret and that the anticipation of regret may influence decision-making, this previous research was largely limited to hypothetical choices with student participants. The current research replicates and extends these findings for real life lottery participation decisions in non-student samples. Four studies are reported in which two lotteries in the Netherlands, the Postcode Lottery and the National State Lottery, were compared. The State Lottery is a traditional lottery in which one has to buy a ticket with a number printed on it. In the Postcode Lottery, one’s postcode is the ticket number, and hence even if not participating one may still find out that one would have won had one played. As our research shows, this particular feedback that is present in the Postcode Lottery but absent in the State Lottery influences the level of anticipated post-decisional regret, and moderates the influence that anticipated regret has on lottery participation. Study 1, 100 street interviews, confirmed our expectations that the Postcode Lottery may elicit regret. Study 2 found under controlled conditions, that people anticipate more regret over not playing when there is feedback about the neighbors winning a prize in the Postcode Lottery than in the State Lottery. However, when this feedback is absent they anticipate equal amounts of regret over not playing. Study 3 replicated these findings for regret, while showing that the two lotteries do not differ with respect to envy and jealousy, emotions that might also be invoked in this context. Study 4 validated that, as we predicted, anticipations of post-decisional regret influence decisions to play the Postcode lottery, but not the State Lottery. These findings demonstrate the external and discriminant validity of anticipated regret for decision-making, and indicate its pragmatic relevance. The implications or recent developments in regret research are discussed.     

Post-decision consolidation over time as a function of gain or loss of an alternative

Post-decision consolidation processes were studied in a two-stage lottery design. School children (1) rated the attractiveness of audiotape head sets, (2) decided for which of two head sets they would like to get a lottery ticket, (3) threw a dice to determine if they got a lottery ticket in the preferred lottery or not, and (4)drew a ticket in the final lottery. Before and after each of these stages ratings were obtained of the attractiveness of the alternatives on four attributes. The results were interpreted in terms of Differentiation and Consolidation Theory. Post-decision consolidation appeared immediately after the outcome of the dice throw. Subjects who won a lottery ticket consolidated their prior decision to a greater degree than those who lost. The effect was so strong for the former group that a pre-decision attractiveness disadvantage was restructured to a post-decision advantage. Folowing the decision, consolidation remained at approximately the level reached immediately after the dice throw for losers and winners, respectively, but with an increasing trend over time for winners. Even following a final loss of an audiotape headset the level of consolidation was maintained.     

Recognizing the Threat Posed by an Incestuous Parent to the Victim's Siblings. Part II: Improving Legal Responses

Many courts refuse to protect the siblings of an incest victim even when faced with unmistakable evidence that they are at risk, arguing that no one can predict what will happen. For instance, some courts believe that a parent who molests his stepchild is unlikely to victimize biological offspring, while others believe that a father who violates a daughter will not also victimize sons. Although judges have relied principally on intuition, a substantial body of empirical studies can help them to better assess a sibling's risk. In Part I, I argued that once a parent establishes the first sexual relationship, other children in the family should be considered at risk. Nonetheless, not all children in the household face identical risks of molestation. In this paper, I continue this theme and argue that a legal presumption should arise that other children are endangered. Further, I maintain that offenders should have an opportunity to rebut this presumption. Without this opportunity, a child who never faced a significant risk of abuse may be removed from his home or unnecessarily lose his ties to a parent. In order to better protect children, I outline how legal decisions can better reflect what is known about child victimization.     

A Pragmatic Dissolution of Harman's Paradox

There is widespread agreement that we cannot know of a lottery ticket we own that it is a loser prior to the drawing of the lottery. At the same time we appear to have knowledge of events that will occur only if our ticket is a loser. Supposing any plausible closure principle for knowledge, the foregoing seems to yield a paradox. Appealing to some broadly Gricean insights, the present paper argues that this paradox is apparent only.     

The relationship between lottery ticket and scratch‐card buying behaviour,personality and other compulsive behaviours

The study examines how demographics, other forms of compulsive behaviour and personality are related to the buying frequency and compulsiveness in lottery tickets and scratch‐cards. An integrative framework is developed and tested in a sample of respondents. Results indicated that the buying compulsivenesses in lottery tickets and scratch‐cards have the same correlates. The buying compulsivenesses in both lottery tickets and scratch‐cards were found to be positively related to cigarette consumption and the extraversion dimension of personality and negatively related to the agreeableness and intellect dimensions of personality. Copyright © 2002 Stewart Publications Ltd.     

The effects of questionnaire length and lottery ticket inducement on the response rate in mail surveys

Abstract

As part of a study on functional gastrointestinal disorders in the Australian community, we surveyed 500 subjects to test the effects of questionnaire length and lottery inducement on the response rate in mail surveys. By random allocation, n = 124 subjects received a short form questionnaire (28 pages) with a lottery ticket, n = 126 received a short form with no lottery ticket, n= 124 received a long form (32 pages) with a lottery ticket and n= 126 received a long form with no lottery ticket. The overall response rate for the study was 74%. The response rates for the short (76.8%) versus long (71.2%) form and lottery ticket (74.2%) versus no lottery ticket (73.8%) were not significantly different. Significantly more short forms compared with longer forms were received after each stage of the follow-up protocol. A long questionnaire can however be successfully used in survey research.     

On “Epistemic Permissiveness”

In ??Epistemic Permissiveness??, Roger White presents several arguments against Extreme Permissivism, the view that there are possible cases where, given one??s total evidence, it would be rational to either believe P, or to believe ??P. In this paper, we carefully reconstruct White??s arguments and then argue that they do not succeed.     

Sarah Palin, A Nation Object(ifie)s: The Role of Appearance Focus in the 2008 U.S. Presidential Election

In 2008, Republican John McCain and his running mate, Sarah Palin, lost the U.S. presidential election to Barack Obama and his vice presidential candidate, Joe Biden. During the campaign, Palin??s physical appearance, including her reported $150,000 makeover, received extensive media coverage. But, could the focus on her appearance have impacted the outcome of the election? Several lines of laboratory research suggest that this focus may have been detrimental to the Republican ticket because 1) it likely undermined perceptions of Palin??s competence, warmth and morality, and 2) it may have increased Palin??s focus on her own appearance, which, consistent with research on self-objectification, likely impaired the competency of her actual performance. Voting research supports the importance of candidates?? perceived competence and character. Thus, while acknowledging the diverse influences on an election??s outcome, a strong empirical case can be made that people objected to Sarah Palin (and therefore, John McCain), in part, because she was objectified. In contrast, there is no evidence to suggest that men suffer these same consequences when others, or they themselves, focus on their appearance. Therefore, it is not likely that the Democratic Obama-Biden ticket was hurt by these same factors.     

An empirical analysis of the characteristics of drivers who are ticketed for traffic offences

This study uses a unique individual-level dataset that merges Israeli census data with official information on traffic tickets issued over a period of seven years in order to explore the socio-demographic characteristics of drivers who receive traffic tickets. The dataset included 409,051 drivers who received a total of 830,763 traffic tickets. The results indicate that about 60% of drivers received at least one ticket during the study period. However, drivers who received tickets were not distributed evenly in society. Of those with the most tickets, 93% were male, and half were in the youngest group of drivers studied. The effect of socioeconomic status appears to differ across different types of offenses. Implications and suggestions for future research are discussed.     

Self-serving judgments about winning the lottery

Although myths and stereotypes about lottery winners tend to be negative (e.g., winners become extravagant), people continue to spend billions of dollars buying lottery tickets in the hope of winning. The authors applied findings from the self-enhancement literature to understand this paradox. Eighty college students received class credit for their participation, in which they read a scenario that asked them to imagine that they, or a target other, had won a lottery. Participants' responses to a 34-item questionnaire displayed a self-serving bias, such that changes to the self were expected to be more positive than changes to the other. For several items, this effect was moderated by the participant's gender. The present research indicates that the pervasive tendency to display self-serving biases can apply to future-oriented processing, an under-researched topic.     

The Presence of Odd Pricing in the Texas State Lottery1

We examined 443 drawings from the Texas state lottery from 1992 to 1997 to determine whether odd pricing effects would be found in multimillion-dollar lotteries. Specifically, we predicted that many more lottery tickets than expected would be purchased when the jackpot amount was $10 million than when it was $9 million. Three findings emerged. First, the higher the jackpot, the more tickets were purchased. Second, odd pricing effects were found at $10 million such that approximately 670,000 more tickets were purchased than expected. Third, controlling for the jackpot amount, there were approximately 620,000 fewer tickets purchased for each drawing per year. This final finding provides evidence that people are becoming less interested in multimillion-dollar lotteries.     

Subjective relative income and lottery ticket purchases

Despite a return of only $.53 on the dollar, state lotteries are extremely popular, especially among the poor, who play the most but can least afford to play. In two experiments conducted with low‐income participants, we examine how implicit comparisons with other income classes increase low‐income individuals' desire to play the lottery. In Experiment 1, participants were more likely to purchase lottery tickets when they were primed to perceive that their own income was low relative to an implicit standard. In Experiment 2, participants purchased more tickets when they considered situations in which rich people or poor people receive advantages, implicitly highlighting the fact that everyone has an equal chance of winning the lottery. Copyright © 2007 John Wiley & Sons, Ltd.     

Knowledge,safety, and Gettierized lottery cases: Why mere statistical evidence is not a (safe) source of knowledge

The lottery problem is the problem of explaining why mere reflection on the long odds that one will lose the lottery does not yield knowledge that one will lose. More generally, it is the problem of explaining why true beliefs merely formed on the basis of statistical evidence do not amount to knowledge. Some have thought that the lottery problem can be solved by appeal to a violation of the safety principle for knowledge, i.e., the principle that if S knows that p, not easily would S have believed that p without p being the case. Against the standard safety‐based solution, I argue that understanding safe belief as belief that directly covaries with the truth of what is believed in a suitably defined set of possible worlds forces safety theorists to make a series of theoretical choices that ultimately prevent a satisfactory solution to the problem. In this way, I analyze several safety principles that result from such choices—the paper thus gives valuable insights into the nature of safety—and explain why none solves the lottery problem, including their inability to explain away Gettierized lottery cases. On a more positive note, I show that there is a viable solution in terms of safety if we get rid of the unquestioned assumption that safe beliefs directly track the truth. The alternative is a conception of safe belief according to which what safe beliefs directly track is the appropriateness of the circumstances and, indirectly, the truth. The resulting safety principle, I argue, explains why mere statistical evidence is not a safe source of knowledge.     

Paying the Way: The Ticket to Gender Equality in Sports

Past research shows that consumers tend to equate higher prices with higher value. However, it remains unclear whether consumers of athletic events follow the predictions of equity theory when attributing value to particular teams. We conducted 3 studies to investigate the existence and consequences of a disparity between men's and women's college basketball ticket prices. In Study 1, a survey of 303 NCAA Division I programs demonstrated that the gender of a basketball team is a primary indicator of the price of a ticket, such that women's tickets are significantly less expensive than men's tickets nationwide, even after controlling for a number of contextual factors (e.g., win–loss records, size of the schools). Consistent with equity theory, Studies 2 and 3 revealed that such a price disparity can result in lower evaluation of women's teams than men's. These findings indicate a need to consider the costs and benefits of maintaining differences in ticket prices within a context of gender inequity.     

Lotteries,Quasi-Lotteries,and Scepticism

I seem to know that I won't experience spaceflight but also that if I win the lottery, then I will take a flight into space. Suppose I competently deduce from these propositions that I won't win the lottery. Competent deduction from known premises seems to yield knowledge of the deduced conclusion. So it seems that I know that I won't win the lottery; but it also seems clear that I don't know this, despite the minuscule probability of my winning (if I have a lottery ticket). So we have a puzzle. It seems to generalize, for analogues of the lottery-proposition threaten almost all ordinary knowledge attributions. For example, my apparent knowledge that my bike is parked outside seems threatened by the possibility that it's been stolen since I parked it, a proposition with a low but non-zero probability; and it seems that I don't know this proposition to be false. Familiar solutions to this family of puzzles incur unacceptable costs—either by rejecting deductive closure for knowledge, or by yielding untenable consequences for ordinary attributions of knowledge or of ignorance. After canvassing and criticizing these solutions, I offer a new solution free of these costs.

Knowledge that p requires an explanatory link between the fact that p and the belief that p. This necessary but insufficient condition on knowledge distinguishes actual lottery cases from typical, apparently analogous ‘quasi-lottery’ cases. It does yield scepticism about my not winning the lottery and not experiencing spaceflight, but the scepticism doesn't generalize to quasi-lottery cases such as that involving my bike.