Anarchism (not to be confused with strains of modern faux-anarchism and the spurious adoption of the terminology from right-wing individualists such as “anarcho”-capitalists and the “Libertarian” Party) is an anti-authoritarian political philosophy with its modern roots in the French Revolution and the work of William Godwin, and its later development and formulation with theorists such as Joseph Déjacque (who first coined the term ‘libertarian’ as a political term and synonym for anarchism) Pierre-Joseph Proudhon, Mikhail Bakunin, Errico Malatesta, Peter Kropotkin, and Murray Bookchin.
The core tenet of anarchism is that authority, or dominion of one person over another, is undesirable and harmful, and as such has a heavy burden of justification. Social relations and institutions are critically analysed with this anti-authoritarian tenet, and it is argued that top-down hierarchical institutions, and social relations where there is a fundamental asymmetry of power. should be replaced by bottom-up forms of organisation, free associations, and institutions where social power is largely egalitarian (to the greatest extent possible).
Anarchism does not preclude leadership or expert authority, in fact, one can argue that recognition for expert authority and the elevation of suitably expert leaders, is one of the things our current society does not do well. (Think Donald Trump. GW Bush. or even Steve Ballmer.)
The Tea Party is a corporate funded astroturf movement full of useful idiots, largely ignorant, and with no coherent theoretical understanding of the system they live in. Consequently, they are able only to repeat slogans and clichés, and unwittingly promote ideas and policies that suit the plutocrats that funded their movement in the first place. They are the populist face of some broadly “Libertarian” policies, like lowering taxes on the rich, and gutting public spending—because that’ll increase their “freedom”.
The sort of individualism espoused by Tea Party and American “Libertarianism” can be summed up with this quote:
“Individualism is, in theory, a kind of Anarchy without cooperation. It is therefore no better than a lie, because liberty is not possible without Solidarity, without cooperation. The criticism which Individualists pass on government is merely the wish to deprive it of certain functions, to hand them over virtually to the capitalists.” —Errico Malatesta.