Possibly. However anarchists don't just say "don't vote", we say "organise" as well. Apathy is something anarchists have no interest in encouraging. So, "[i]f the anarchists could persuade half the electorate to abstain from voting this would, from an electoral point of view, contribute to the [electoral] victory of the Right. But it would be a hollow victory, for what government could rule when half the electorate by not voting had expressed its lack of confidence in all governments?" [Vernon Richards, The Impossibilities of Social Democracy, p. 142]
In other words, whichever party was in office would have to rule over a country in which a sizeable minority, even a majority, had rejected government as such. This would mean that the politicians "would be subjected to real pressures from people who believed in their own power" and acted accordingly. So anarchists call on people not to vote, but instead organise themselves and be conscious of their own power both as individuals and as part of a union with others. Only this "can command the respect of governments, can curb the power of government as millions of crosses on bits of paper never will." [Ibid.]
As Emma Goldman pointed out, "if the Anarchists were strong enough to swing the elections to the Left, they must also have been strong enough to rally the workers to a general strike, or even a series of strikes. . . In the last analysis, the capitalist class knows too well that officials, whether they belong to the Right or the Left, can be bought. Or they are of no consequence to their pledge." [Vision on Fire, p. 90]
The mass of the population, however, cannot be bought off and if they are willing and able to resist then they can become a power second to none. Only by organising, fighting back and practising solidarity where we live and work can we really change things. That is where our power lies, that is where we can create a real alternative. By creating a network of self-managed, pro-active community and workplace organisations we can impose by direct action that which politicians can never give us from Parliament. And only such a movement can stop the attacks upon us by whoever gets into office. A government (left or right) which faces a mass movement based upon direct action and solidarity will always think twice before proposing cuts or introducing authoritarian laws.
Of course, all the parties claim that they are better than the others and this is the logic of this question — namely, we must vote for the lesser evil as the right-wing in office will be terrible. But what this forgets is that the lesser evil is still an evil. What happens is that instead of the greater evil attacking us, we get the lesser evil doing what the right-wing was going to do. And, since we are discussing the "lesser evil," let us not forget it was the "lesser evil" of the Democrats (in the USA) and Labour (in the UK) who introduced the monetarist and other policies that Reagan and Thatcher made their own (and we may add that the US Air Traffic Controllers union endorsed Reagan against Carter in 1980 because they thought they would get a better deal out of the Republicans. Reagan then went on to bust the union once in office). Simply put, we cannot expect a different group of politicians to react differently to the same economic and political pressures and influences.
So, voting for other politicians will make little difference. The reality is that politicians are puppets. As we argued above (in section J.2.2) real power in the state does not lie with politicians, but instead within the state bureaucracy and big business. Faced with these powers, we have seen left-wing governments from Spain to New Zealand introduce right-wing policies. So even if we elected a radical party, they would be powerless to change anything important and soon be forced to attack us in the interests of capitalism. Politicians come and go, but the state bureaucracy and big business remain forever!
Therefore we cannot rely on voting for the lesser evil to safe us from the possible dangers of a right-wing election victory brought about by abstentionism. All we can hope for is that no matter who gets in, the population will resist the government because it knows and can use its real power - direct action. For the "only limit to the oppression of government is the power with which the people show themselves capable of opposing it." [Errico Malatesta, Life and Ideas, p. 196] Hence Vernon Richards:
"If the anarchist movement has a role to play in practical politics it is surely that of suggesting to, and persuading, as many people as possible that their freedom from the Hilters, Francos and the rest, depends not on the right to vote or securing a majority of votes 'for the candidate of ones choice,' but on evolving new forms of political and social organisation which aim at the direct participation of the people, with the consequent weakening of the power, as well of the social role, of government in the life of the community." [The Raven, no. 14, pp. 177-8]
We discuss what new forms of political and social organisations anarchists encourage in section J.5.