David Nolan first published the current version of the chart in an article called "The Case for a Libertarian Political Party" in the August 1971 issue of The Individualist, the monthly magazine of the Society for Individual Liberty (SIL). In December of 1971, he helped to start the group that would become the Libertarian Party.
The advocates and writers of these quizzes are most often libertarian, and a common remark by them about their tests is that people who are libertarians inside and didn't know it will discover their true political leanings. The detractors of the Nolan Chart are most often people who accuse people with libertarian beliefs of using it to further their agenda and gain converts to their party and political movement. For example, the questions in such quizzes are often worded in such a way to encourage people to select the "libertarian" answer because all other answers are portrayed so negatively, or the answers meant to indicate a libertarian temperament are so vague or broad that one could easily agree with them while holding different views.
The libertarian conception of freedom is perceived by some as tending toward anarchy. Others see it as driven by excessive individualism that actually detracts from social freedom. In essence, they claim the "chart" exists only to distance the term "libertarianism" from the older terms of anarchism and socialism, the latter of which draws polemic connections to communism, which itself draws polemic connections to totalitarianism.
A similar criticism of the chart is that the terms "authoritarianism" and "liberalism," as used to describe opposing stances on the y-axis of "personal freedom," do not easily apply to some prominent contemporary social issues (although these terms were not originally used by Nolan, they have become popular with followers of his chart system). For example, proponents of strict gun control are generally social liberals, who see fewer guns on the streets as promoting individual safety and thus individual liberty. At the same time, opponents of gun control see restrictions on certain firearms as an infringement on their personal liberties and a step towards totalitariansim. Similar problems emerge from other social issues such as abortion, where the debate centers on whether the "right" to have an abortion is more or less important than the "rights" of the unborn child. In both of these examples, both sides tend to argue that their stance on the issue maximises total liberty. Thus the division between "liberal" and "authoritarian" is of little use on these issues, and the debate instead often divides people in terms of other exogenous factors such as their religious beliefs. This, some argue, leaves the effectiveness of the chart somewhat compromised. (However, a counterargument is that the liberal and authoritarian quadrants are not in direct opposition. Anyone who moves toward the bottom of the chart but still favors liberty will most likely end up on the right quadrant. It is already established that liberals and conservatives have different ideas of liberty - positive liberty and negative liberty.)
Other critics argue that the libertarian definition of economic and personal "freedom" is incorrect or flawed, and that non-libertarian ideologies actually give people more freedom than libertarianism does. One such argument is that freedom from government intervention in the economy does not assure individual freedom within the private sector, and that government may preserve individual freedom against non-governmental powers. (This is the case Noam Chomsky makes when he refers to "private tyranny." ) Nolan's usage of "populism" shows that he rejects this argument.
The x-axis of "economic freedom" assumes a choice between a strongly state-regulated economy ("low economic freedom") and free-market capitalism ("high economic freedom"). This completely ignores the existence of libertarian socialism and most branches of anarchism, who are opposed both to the state and to capitalism. Anarchists and libertarian socialists do not want any kind of state intervention in the economy, yet they are also vehemently opposed to private property over the means of production and wish to give the workers direct collective control over the economy. They see themselves as promoting economic freedom, but certainly not in the capitalist sense that is used in the Nolan chart.
In addition to these ideological objections, the "How People Have Scored" section gives results that do not seem to be representative of most Americans' political beliefs. Currently, 34.76% of test takers have scored Libertarian, compared to 30.26% who have scored Centrist. This overrepresentation of Libertarians could be a reflection of the sample of people viewing the website, however there were also more test takers who scored Statist (8.67%) than Conservative (7.64%).
A few of the people who oppose the use of the Nolan Chart are strong libertarians, Objectivists or other advocates of laissez-faire capitalism who believe that the political spectrum need be portrayed only through one dimension, but not the traditional Left/Right one. They propose an axis with totalitarianism/authoritarianism (statism) at one end, and libertarianism at the other end—something similar to the first diagonal of the Nolan Chart. They insist that all types of government intervention, in any areas, are the same.