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In this paper we investigate four prominent LP systems, the systems<jats:bold>O, P<\/jats:bold>,<jats:bold>Z<\/jats:bold>, and<jats:bold>QC<\/jats:bold>. These systems differ in the number of inferences they licence (<jats:bold>O<\/jats:bold>\u2282 P \u2282<jats:bold>Z<\/jats:bold>\u2282<jats:bold>QC)<\/jats:bold>. LP systems that license more inferences enjoy the possible<jats:italic>reward<\/jats:italic>of deriving more true and informative conclusions, but with this possible reward comes the<jats:italic>risk<\/jats:italic>of drawing more false or uninformative conclusions. In the first part of the paper, we present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of<jats:italic>reward<\/jats:italic>versus<jats:italic>risk<\/jats:italic>. Our results suggest that system<jats:bold>Z<\/jats:bold>offers the best balance.<\/jats:p>","DOI":"10.1017\/s1755020312000184","type":"journal-article","created":{"date-parts":[[2012,7,5]],"date-time":"2012-07-05T03:25:27Z","timestamp":1341458727000},"page":"574-612","source":"Crossref","is-referenced-by-count":13,"title":["REWARD VERSUS RISK IN UNCERTAIN INFERENCE: THEOREMS AND SIMULATIONS"],"prefix":"10.1017","volume":"5","author":[{"given":"GERHARD","family":"SCHURZ","sequence":"first","affiliation":[]},{"given":"PAUL D.","family":"THORN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,7,4]]},"reference":[{"key":"S1755020312000184_ref83","first-page":"155","volume-title":"Probability and Inference: Essays in Honor of Henry E. 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