Publications (Alan D. Taylor)

Books

1. Structural Properties of Ideals (with J. Baumgartner and S. Wagon), Warszawa, Poland: Dissertationes Mathematicae (1982), ISBN 83-01-01506-3.
2. Mathematics and Politics: Strategy, Voting, Power, and Proof, New York: Springer-Verlag (1995), ISBN 0-387-94391-9 and 0-387-94500-8. Second edition (with A. Pacelli), New York: Springer-Verlag (2008).
3. Fair Division: From Cake-Cutting to Dispute Resolution (with S. Brams), Cambridge, England: Cambridge University Press (1996), ISBN 0-521-55390-3 and 0-521-55644-9.
4. Simple Games: Desirability Relations, Trading, and Pseudoweightings (with W. Zwicker), Princeton: Princeton University Press (1999), ISBN 0-691-00120-0.
5. The Win-Win Solution: Guaranteeing Fair Shares to Everybody (with S. Brams), New York: Norton (1999), ISBN 0-393-04729-6 Translations have appeared in China, Japan, Russia, Brazil, Korea, and Portugal.
6. Social Choice and the Mathematics of Manipulation, Cambridge England: Cambridge University Press (2005), ISBN 0-521-81052-3 and 0-521-00883-2.
7. The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems (with C. Hardin), New York: Springer-Verlag (2013), ISBN 978-3-319-01332-9.

Articles and Book Chapters

1. A canonical partition relation for finite subsets of Journal of Combinatorial Theory (A) 21 (1976), 137–146.
2. On splitting stationary subsets of large cardinals (with J. Baumgartner and S. Wagon), Journal of Symbolic Logic 42 (1977), 203–214.
3. Partitions of pairs of reals, Fundamenta Mathematicae XCLX (1978), 51–59.
4. Partition theorems and ultrafilters (with J. Baumgartner), Transactions of the American Mathematical Society 241 (1978), 283–309.
5. Ideals on uncountable cardinals (with J. Baumgartner and S. Wagon), Logic Colloquium 77, North Holland (1978), 67–77.
6. Regularity properties of ideals and ultrafilters, Annals of Mathematical Logic 16 (1979), 35–55.
7. On saturated sets of ideals and Ulam’s problem, Fundamenta Mathematicae CIX (1980), 37–53.
8. Bounds for the disjoint unions theorem, Journal of Combinatorial Theory (A) 20 (1981), 339–344.
9. Diamond principles, ideals and the normal Moore space problem, Canadian Journal of Mathematics XXXIII (1981), 282–296.
10. A note on a lemma of Shelah concerning stationary sets (with A. Mekler and D. Pelletier), Proceedings of the American Mathematical Society 83 (1981), 764–768.
11. Saturation properties of ideals in generic extensions I (with J. Baumgartner), Transactions of the American Mathematical Society 270 (1982), 557–574.
12. Saturation properties of ideals in generic extensions II (with J. Baumgartner), Transactions of the American Mathematical Society 271 (1982), 587–609.
13. A note on van der Waerden’s theorem, Journal of Combinatorial Theory (A) 33 (1982), 215–219.
14. Negative partition relations for ultrafilters on uncountable cardinals (with A. Kanamori), Proceedings of the American Mathematical Society 92 (1984), 83–89.
15. Separating ultrafilters on uncountable cardinals (with A. Kanamori), Israel Journal of Mathematics 47 (1984), 131–138.
16. On the cardinality of reduced power set algebras, Proceedings of the American Mathematical Society 103 (1988), 277–280.
17. Separating Collections, Fundamenta Mathematicae 133 (1989), 135–145.
18. Diverse homogeneous sets (with A. Blass and P. Erdös), Journal of Combinatorial Theory (A) 59 (1992), 312–317.
19. A characterization of weighted voting (with W. Zwicker), Proceedings of the American Mathematical Society 115 (1992), 1089–1094.
20. Weighted voting, multicameral representation, and power (with W. Zwicker), Games and Economic Behavior 5 (1993), 170–181.
21. Divide the dollar (with S. Brams), Theory and Decision 37 (1994), 211–231.
22. An envy-free cake division protocol (with S. Brams), American Mathematical Monthly 102 (1995), 9–18.
23. On envy-free cake division (with S. Brams), Journal of Combinatorial Theory (A) 70 (1995), 170–173.
24. Preference relations and measures in the context of fair division (with J. Barbanel), Proceedings of the American Mathematical Society 123 (1995), 2061–2070.
25. Simple games and magic squares (with W. Zwicker), Journal of Combinatorial Theory (A) 71 (1995), 67–88.
26. Old and new moving-knife schemes (with S. Brams and W. Zwicker), Mathematical Intelligencer 7 (1995), 30–35.
27. Fair division and politics (with S. Brams), PS: Political Science and Politics XXVIII (1995), 697–703.
28. Social choice and the Catalan numbers (with S. Young and W. Zwicker), Mathematics Magazine 68 (1995), 331–342.
29. A procedure for divorce settlements (with S. Brams), Mediation Quarterly 13 (1996), 191–205.
30. Quasi-weightings, trading, and desirability relations (with W. Zwicker), Games and Economic Behavior 16 (1996), 331–346.
31. Social Choice: The Impossible Dream, (with S. Brams), chapter in For All Practical Purposes, published by W. H. Freeman under the auspices of COMAP, 4th edition (1996), 5th edition (1999), 6th edition (2002), 7th edition (2005), 8th edition (2008), 9th edition (2011).
32. Fair Division (with S. Brams), chapter in For All Practical Purposes, published by W. H. Freeman under the auspices of COMAP, 4th edition (1996), 5th edition (1999), 6th edition (2002), 7th edition (2005), 8th edition (2008), and 9th edition (2011).
33. A glimpse of impossibility, Perspectives on Political Science 26 (1997), 23–26.
34. A moving-knife solution to the four-person envy-free cake-division problem (with S. Brams and W. Zwicker), Proceedings of the American Mathematical Society 125 (1997), 547–554.
35. Interval measures of power (with W. Zwicker), Mathematical Social Sciences 33 (1997), 23–74.
36. A negotiating strategy (with S. Brams), Corporate Council Magazine 6 (1999), 47–50.
37. Logic and Modeling, chapter in For All Practical Purposes, published by W. H. Freeman under the auspices of COMAP, 5th edition (1999).
38. Trading properties and Alexandrov kernels for Boolean functions (with W. Zwicker), Discrete Applied Mathematics 107 (2000), 203–214.
39. The manipulability of voting systems, American Mathematical Monthly109 (2002), 321–337.
40. Introduction to The Geometry of Efficient Fair Division, by Julius Barbanel, Cambridge University Press, 2005, 1–6.
41. A paradoxical Pareto frontier in the cake-cutting context, Mathematical Social Sciences 50 (2005), 227–233.
42. Tight Bounds on Plurality (with N. Srivastava), Information Processing Letters 96 (2005), 93–95.
43. The Manipulability of Voting Systems, chapter in For All Practical Purposes, published by W. H. Freeman under the auspices of COMAP, 7th edition (2005), 8th edition (2008), and 9th edition (2011).
44. Borel separability of the coanalytic Ramsey sets, Annals of Pure and Applied Logic 144 (2006), 130–132.
45. A peculiar connection between the axiom of choice and predicting the future (with C. Hardin), American Mathematical Monthly 115 (2008), 91–96.
46. An introduction to infinite hat problems (with C. Hardin), Mathematical Intelligencer 30 (2008), 20–25.
47. Limit-like predictability for discontinuous functions (with C. Hardin), Proceedings of the American Mathematical Society 137 (2009), 3123–3128.
48. Mathematics and Voting, chapter in La Matematica, vol. 4: Intrecci, ed. Claudio Bartocci and Piergiorgio Odifreddi, Einaudi (2010).
49. Analysis of binary voting algorithms for use in fault-tolerant and secure computing (with K. Kwait, W. Zwicker, D. Hill, S. Wetzonic, and R. Shangping), Proceedings of the IEEE International Conference on Computer Engineering and Systems (2010) 273–285.
50. Minimal predictors in hat problems (with C. Hardin), Fundamenta Mathematicae 208 (2010), 273–285.
51. Prediction problems and ultrafilters on omega, Fundamenta Mathematicae 219 (2012), 111–117.