Abstract 鈥?A common activity in popular culture is the formation of top lists: the top 100 songs of all time Sam Darnold Jersey , the 50 favorite movies, the top 100 movie stars and so on. These top lists are then publicized on radio and on the inter-net. In this paper, which is part research, part expository and part computer simula-tion, we examine the mathematics of form-ing such lists in the situation where there are no measurable head-to-head comparisons and the compilation of the ranked list is formed by respondents鈥?choices. There is an implied assumption that the compiled lists fomr a representative list of a true ranked list. statistical and therefore form a rep-resentative picture of a 鈥渢rue鈥?ranked list. We construct statistical models for these list formations and define a true ranking in two different ways. We then prove several para-doxical results that show non-significant cor-relation between the true ranked list and the compiled list. For example Le'Veon Bell Jersey , we show that there exist populations which contain an item that has a true ranking of number one but for which this item will not appear on any compiled list. These results are related to Arrow鈥檚 impossibility theorem (see [1]) in the theory of elections. A computer simula-tion was conducted in conjunction with the study to determine whether these paradoxes are aberrations. The simulations show that these aberrations only occur with low prob-ability and on average there is a positive but weak correlation between the compiled list and the true ranked list.

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