This is Section a of Chapter 4 of Beyond Classical Marxism.
Democracy is at the core of the sort of “socialist” society which we aim to create. The great Polish-German socialist fighter Rosa Luxemburg stated this clearly in September 1918, when the Bolsheviks were starting to transform their revolution into a dictatorship over the masses parading itself as the “dictatorship of the proletariat”:
“All this shows that ‘the cumbersome mechanism of democratic institutions’ possesses a powerful corrective – namely, the living movement of the masses, their unending pressure. And the more democratic the institutions, the livelier and stronger the pulse-beat of the political life of the masses, the more direct and complete is their influence – despite rigid party banners, outgrown tickets (electoral lists), etc. To be sure, every democratic institution has its limits and shortcomings, things which it doubtless shares with all other human institutions. But the remedy which Trotsky and Lenin have found, the elimination of democracy as such, is worse than the disease it is supposed to cure; for it stops up the very living source from which alone can come the correction of all the innate shortcomings of social institutions. That source is the active, untrammeled, energetic political life of the broadest masses of the people.” (p. 302)
“In place of the representative bodies created by general, popular elections, Lenin and Trotsky have laid down the soviets as the only true representation of the laboring masses. But with the repression of political life in the land as a whole, life in the soviets must also become more and more crippled. Without general elections, without unrestricted freedom of press and assembly, without a free struggle of opinion, life dies out in every public institution, becomes a mere semblance of life, in which only the bureaucracy remains as the active element. Public life gradually falls asleep, a few dozen party leaders of inexhaustible energy and boundless experience direct and rule.” (p. 307) [emphasis added]
(The above two quotations are from The Rosa Luxemburg Reader, edited by Peter Hudis & Kevin B. Anderson (Monthly Review Press, 2004): from “The Russian Revolution” written in September 2018,)
“Democracy” means exactly that: the equal right of everyone to participate in decision-making affecting their lives. It is not, as Leninism teaches us, the dictatorship of the working class over the rest of society (which in practice has actually meant the dictatorship of the Party over the working class and everyone else in society). People must be able to organize to advance their own interests, so long as this doesn’t involve oppressing others. (No, there is not the “right” to oppress LBGTQ people, although such activity will hopefully be countered effectively in a non-oppressive way.) It must be possible to vote a given government out of power, if so desired by the majority. Of course, we cannot allow the wealthy to unduly influence political campaigns; strict campaign contribution limits must be invoked and public funding of electoral campaigns should be created. (A start at such public funding has already taken place in Seattle, with all voters provided with four $25 vouchers which can be contributed to candidates who set a limit on their campaign spending.)
Most importantly, society must take control of the “commanding heights of the economy” (banks, big corporations, etc.) through state ownership of these economic entities. (This is explained in the model of socialism presented in Chapter 5; it is in fact what crucially distinguishes socialism from social democracy.) Small-scale private enterprise is to be allowed to continue indefinitely in the new socialist society, but no longer will the bourgeoisie be able to dominate politically simply through ownership of the means of production. To a much greater extent than now, it will be “one person, one vote” rather than “one dollar, one vote”.