What David Ricardo's "Principles" did for the analysis of political policies, this book does for the analysis of the political processes which create policies in democracies. That is, it calls for the use of diagrams, principles, and simple numerical examples to reason about human behavior in a consistent, reliable, testable, and otherwise standardized manner.
On that reputation, I began to read-- and was immediately surprised by the weakness of the mathematics. There are trivial errors: page 179* contains a sign error in equation (8). The graph on page 180 is far too low-dimensional to represent what the text is discussing. The accompanying text is not much better: equation (4) on page 176 has three fundamental errors: it tries to establish equality between vectors of different lengths, it asserts equality when an equivalence relation is not established, and it mismatches dimensions instead of comparing entry-by-entry (i.e. it should read x_i <= V_i(I_n)). I know this because I followed the footnote citation to my copy of Luce and Raiffa. On page 257 Buchanan and Tullock try to add a count to a percent, resulting in a meaningless value.** Almost all of these issues can be explained from a lack of familiarity with mathematical notation. I began to think that Buchanan and Tullock were merely using mathematical symbols and language to enhance the perceived quality of the argument.*** I was most annoyed when they introduced a partial derivative in Chapter 15 to analyze a constitutional choice utility function of four vaguely defined scalers: "rules for electing members," "basis of representation," "degree of representation," and "the rule through which the legislative assembly shall reach its decisions." I stopped reading the book for two years.
When I came back to it this week, I had a new point of view: the historical one. From the historical point of view, this ill-use of analysis and all the rest was a call to action by two not-quite-mathematicians for the actual mathematical work to be done. Chapter 15 was written in 1961. Buchanan died in 2013, Tullock died in 2014, and, in 2015, Ethereum launched, making smart contracts real. Chapter 15 was vindicated! Everything in this book is similarly vindicated. I was, as they say, missing the forest for the trees.
This monograph is historically important for introducing the quantitative study of political decision-making into a field which tended to focus on the moral decisions of specific leaders or a vaguely conceived notion of "general will." It is not a textbook because (1) it spends much of the text justifying its relevance rather than explaining the theory, (2) it contains a number of technical errors, (3) it does not offer a bank of testable questions, and (4) it does not include any of the wonderful subsequent theory developed and empirical work conducted in this field. Please use a standard textbook if you are teaching a class on public choice. It is also not a popularization, it would be better to read "The Myth of the Rational Voter" if you are curious about public choice economics.
*In "The Collected Works of James M. Buchanan, Vol. 3" ISBN 9780865972186
**Another example comes from page 156: the only actual payoffs are A = (10,0,0), B = (0,5,0), and C = (0,0,1) for farmers a,b, and c. Therefore farmer b can always choose between A or C. Similarly, a with B or C and c with A or B. Any two farmer coalition will therefore always control the outcome (eg. the control set of a,c is {B,C,A,B} -- we do not need to write B twice). The a,b coalition can thus create the outcome (5,5,0) through the simple pattern "BBABBA...", (5,5,0) dominates (5,2.5,0), (5,0,0.5), and (0,2.5,0.5). In this case, c could purchase a defection by offering b the agreement BBBCBBBC... however, a could easily outbid c as far as Bx30ABx30A because a is rewarded ten times what c is. Thus the ab coalition will return. I could go on and on about the errors in this book, but they don't matter.
***Buchanan and Tullock are at their best when using simple arithmetic and diagrams. Chapters 10 and 16 stand up technically and would be worth excerpting.