Frontiers in Psychology AbstractPeople often justify their moral opinions by referring to larger moral concerns (e. g., “It isunfairif homosexuals are not allowed to marry!” vs. “Letting homosexuals matraditions!”). Is there a general agreement about what concerns apply to different moral opinions? We used surveys in the United States and the United Kingdom to measure the perceived applicability of eight concerns (harm, violence, fairness, liberty, authority, ingroup, purity, and governmental overreach) to a wide range of moral opinions. Within countries, argument applicability scores were largely similar whether they were calculated among women or men, among young or old, among liberals or conservatives, or among people with or without higher education. Thus, the applicability of a given moral concern to a specific opinion can be viewed as an objective quality of the opinion, largely independent of the population in which it is measured. Finally, we used similar surveys in Israel and Brazil to establish that this independence of populations also extended to populations in different countries. However, the extent to which this holds across cultures beyond those included in the current study is still an open question.

Combinatorics, Probability and Computing, 1-21. doi:10.1017/S096354831800055X, Cambridge University Press. Abstract An n × n partial Latin square P is called α-dense if each row and column has at most αnnon-emp times in . An × array where each cell contains a subset of {1,…, } is a (, ) -array if each symbol occurs at most times in each row and column and each cell contains a set of size at most . Combining the notions of completing partial Latin squares and avoiding arrays, we prove that there are constants , > 0 such that, for every positive integer , if is an -dense × partial Latin square, is an × -array, and no cell of contains a symbol that appears in the corresponding cell of , then there is a completion of that avoids ; that is, there is a Latin square that agrees with on every non-empty cell of , and, for each , satisfying 1 ≤ , ≤ , the symbol in position (, ) in does not appear in the corresponding cell of .

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