Henry E. Kyburg Jr.'s lottery paradoxKyburg, H. E. (1961). Probability and the Logic of Rational Belief, Middletown, CT: Wesleyan University Press, p. 197. arises from  considering a fair 1,000-ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that some ticket will win. Suppose that an event is very likely only if the probability of it occurring is greater than 0.99. On these grounds it is presumed  rational to accept the proposition that ticket 1 of the lottery will not win. Since the lottery is fair, it is rational to accept that ticket 2 will not win either —indeed , it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 will not win, accepting that ticket 2 will not win, and so on until accepting that ticket 1,000 will not win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins. The lottery paradox was designed to demonstrate that three attractive principles governing rational acceptance lead to contradiction , namely that It is rational to accept a proposition that is very likely true , It is irrational to accept a proposition that is known to be inconsistent , and is jointly inconsistent  If it is rational to accept a proposition A and it is rational to accept another proposition A', then it is rational to accept A and A'.
The lottery paradoxKyburg, H. E. (1961). Probability and the Logic of Rational Belief, Middletown, CT: Wesleyan University Press, p. 197. arises from Henry E. Kyburg Jr. considering a fair 1,000-ticket lottery that has exactly one winning ticket. If that much is known about the execution of the lottery , it is then rational to accept that some ticket will win. Suppose that an event is very likely only if the probability of it occurring is greater than 0.99. On those grounds, it is presumed to be rational to accept the proposition that ticket 1 of the lottery will not win. Since the lottery is fair, it is rational to accept that ticket 2 will not win either . Indeed , it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 will not win, accepting that ticket 2 will not win, and so on until accepting that ticket 1,000 will not win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins. The lottery paradox was designed to demonstrate that three attractive principles governing rational acceptance lead to contradiction : It is rational to accept a proposition that is very likely true . It is irrational to accept a proposition that is known to be inconsistent and is jointly inconsistent . If it is rational to accept a proposition A and it is rational to accept another proposition A', it is rational to accept A and A'.
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