Why veto the bill based on governor-s decision rule


The governor of a large, northeastern state is trying to decide whether to veto a bill that she opposes that has been passed by the state legislature. As a politically minded actor, she has adopted the decision rule that if the bill has a probability greater than .5 of becoming a law even if she vetoes it, then she will sign the bill despite her opposition (and no doubt share credit for its passage). There are two ways in which the bill may become law over her veto. First, the state legislature may overturn her veto by voting resoundingly for passage. The governor estimates the probability of this outcome to be .3. The second way is through a referendum involving the voters of the state. If she vetoes the bill, and the legislature does not pass it over her veto, she further estimates that the probability of a referendum movement occurring is .9 (a powerful interest group supports the bill). She further estimates that the probability that the referendum movement will obtain the required number of signatures to qualify for a vote of the citizens of the state is .75.  Finally, she estimates that given a referendum, the voters have a 50/50 chance (P = .5) of approving the bill. Based on the governor's decision rule, should she veto the bill? 

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Mathematics: Why veto the bill based on governor-s decision rule
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