The premise of the book is that, despite the myriad flaws of democracy, it nevertheless has a number of features that make it the most successful system of governance. Oppenheimer and Edwards split the book into two parts. The first part describes four flaws of democracy: 1) voters typically don't know about the issues at stake in elections, 2) voters are generally "irrational" decision-makers even when they do have some knowledge, 3) it's very hard to design a representative democratic system (because of biases inherent in e.g. districting, election dates, etc.), and 4) for the elected representatives, it can be very hard to know what voters really want. Nevertheless, as the second part discusses, democracies are very successful overall--in terms of peace and prosperity for their citizens--compared with other systems of government, mostly because they set up good incentives for voters and representatives.
This general account sounds very reasonable overall, and DDI is a fun, easy read. It's filled with straightforward and clear examples (often from sports) that make the phenomena easy to understand. Danny wanted to call his book "DemoCrazy," and that nicely captures both the thesis and the tone of the book.
Despite how much I liked the book, I want to make two slightly critical points. First, DDI spends only a short amount of time on how to solve the problems it outlines (or even whether they are soluble). This is fine for a short book, but at times I worried that the two-part organization--"democracy is surprisingly crazy but yet works surprisingly well"--made the authors equate different kinds of problems that should be distinguished. While the quirks of human cognition--like our susceptibility to framing effects--aren't something that we can correct, other problems can be addressed, such as flaws in redistricting. While, as Oppenheimer and Edwards point out, there are many different metrics by which to assess the fairness of a redistricting scheme, some redistricting schemes aren't fair. There not be one single perfect solution, but we can definitely do better. If redistricting choices are made by partisan groups, then they are especially likely to be unfair.
Second, DDI doesn't distinguish between problems that cause bias and those that cause variance. Consider elections as a method for estimating what governance a group of people wants. (This is potentially problematic but let's go with it for now). Let's start with the simplest case. Imagine Alice, a single individual. Alice has perfect knowledge of the policy landscape. She is a rational decision-maker. Presented with an infinite array of possible representatives who vary in their stated policies, she can then easily choose the one whose policies minimize her regret.
Now move away from this world in a few different directions. Imagine that she has only a random sample of a few possible representatives in each election. And she has only partial knowledge of each representative's position (assuming facts are sampled at random). Now finally, imagine there are thousands of Alices, each making their own decisions in accord with their own interest based on their own partial knowledge of the issues. It's easy to see that each of these lead to higher average regret for Alice (variance). But there is no systematic bias in the system yet. This seems like a reasonable model of some of the issues that DDI discusses, especially problems of imperfect knowledge on the part of the voters and representatives.
But there are other problems that would lead to bias, rather than variance. Imagine that the election is rigged, Alice's district is gerrymandered, her access to information is systematically manipulated. All of these systematically change the long-run fairness of the system. Of course we would want to reduce variance if we could, but these kinds of biasing factors seem much more dire. Distinguishing between the two feels important.
Outside of these minor concerns, DDI is a clear and engaging look at the topic. It's very well written also. I recommend it to anyone curious about the intersection of psychology and politics.