The book complains that minority candidates win office thanks to the minority-bias in the electoral system. What the book fails to acknowledge is that candidates' campaign strategies respond to the electoral system. If one changes the game, players change their play. If a president who has won electoral college but has lost the popular vote had to win the popular vote instead, he would have likely changed his strategy and would have won the election anyway. As a result, the book's counterfactuals are unpersuasive.
The book acknowledges that liberal democracies combine two ingredients: the liberal one (which protects minorities) and the democratic one (which protects majorities). This is an easy (but valuable) observation to make (over and over again). What is hard is to determine the optimal proportion in which the two ingredients ought to be mixed. The book makes little progress on that front and instead argues for the majoritarian extreme.
By examining a series of case studies, the book argues that the current balance between liberalism and democracy must be wrong simply because the policies that the book's authors favour end up being blocked by minorities. This is not a principled argument.
The book argues that the rules of the game must change, but it fails to persuade why doing so would make any difference. Games with different rules can lead to the same outcomes. Games with "nicer-looking" rules can lead to "worse" outcomes once one takes into account how players adapt their play to the rules. Amending the Constitution to suit the political sentiment of the moment in a small town in Massachusetts could erode the legitimacy of the Constitution while delivering precious little in benefits from purportedly superior outcomes.
The electoral system in the U.S. is biased in favour of representing places and away from representing people. (The bias towards places has also been noted by urban economist Ed Glaeser, who bemoaned the fact that urban policies are often designed to revitalise places where no one lives instead of focusing on helping people move wherever they might flourish.) There ought to be a normative argument for over-representing empty spaces, but it is nowhere to be found in the book. Perhaps, by over-representing a place, one somehow takes into account the welfare of the future generations who will inhabit this place.
The book claims, without proof, that proportional representation is the only true form of democracy. This idea is controversial. (The Supreme Court rejected it in its deliberations on gerrymandering.) The idea requires a justification that would go beyond "Europeans do it."
The book claims it ought to be easy to vote, but, once again, does not argue the case. Do not barriers help to ensure that only those who care deeply enough about the outcome bother to vote and are heard?
Here is a possible argument for making it easy to vote: Today, political candidates waste too much time and money trying to turn out voters in ever greater numbers. If voting were easy, then, instead of competing in the zero-sum (negative-sum?) game of turnout, the candidates would compete on policies. Policy competition, presumably, is a positive-sum game.
The book's strength is in putting present-day politics into a historical perspective. But of its conclusions, the book will not persuade anyone who is not already a convert.