1 The share of the population in the lower class will increase.
2 The share of the population in the middle class will go to zero.
3 The number of people in the upper class will converge towards a very small number.
Horkheimer can hardly be made in stand in for '20th-century Marxists', whatever his views, acknowledgements or revisions.
But let's take the predictions.
The share of the population in the lower class will increase.
Is the 'lower class' a Marxist term ? Marx refers to 'the proletarian class', 'agricultural labourers', 'the lumpenproletariat', 'the unemployed'. He offers specific predictions for each of these, not for 'the lower class'.
If we make these distinctions, it does appear quite definitely that Marx predicted that the share of the population in the 'lower class' will increase. He says that all landowners will eventually disappear, that the feudal aristocracy will be destroyed by foreign competition, and that entire sections of the ruling class will be drawn into the proletarian class.
The share of the population in the middle class will go to zero.
Marx thinks this will happen along two routes : (a) the smaller capitalists or bourgeoisie will 'go under' to the larger under the impact of competition, and (b) the bourgeoisie will be eliminated as a class in the proletarian revolution.
So : another authentically Marxist prediction
The number of people in the upper class will converge towards a very small number.
Marx predicts that joint-stock companies will emerge as the new aristocracy, that the moneylending class will disappear, that all landowners will also disappear, and that larger capitalists will absorb or put smaller capitalists out of business. That indicates a relatively small 'upper class'.
Was the failure of these predictions acknowledged by 20th-century Marxists ?
I'm not at all dismissive of Horkheimer but it would be interesting if we could add to the number of Marxists who were clear-sighted enough to perceive that something had gone wrong with Marx's predictions.
I add just one point, though. Marx does refer on occasion (e.g. in Capital, I) to 'the iron laws of history' but in more reflective moments he recognised that his 'laws' were not inevitabilities but actually 'trends'. This claim is supported by the following quotation :
"He [my critic] feels himself obliged to metamorphose my sketch of the genesis of
capitalism in Western Europe into an historico-philosophical theory of the marche
generale imposed by fate on every people, whatever the historic circumstances in which
it finds itself, in order that it may ultimately arrive at the form of economy which will
ensure, together with the greatest expansion of the productive powers of social labor,
the most complete development of man. But I beg his pardon. (He is both honoring and
shaming me too much.)"
Marx to the Editor of a Russian Joumal, 1877: Correspondence of Marx and Engels,
ed. by Dona Torr (Intemational, 1934), p. 35. (Cited in Richard Hudelson, 'Popper's Critique of Marx', Philosophical Studies: An International Journal for Philosophy in the Analytic
Tradition, Vol. 37, No. 3 (Apr., 1980), pp. 259-270 : 270.)
Marx and Marxists can reasonably argue that given that Marx was arguing from trends and not laws, his projection of predictions from trends doesn't disprove the trends; it just shows the specific predictions were wrong or ill-timed. In other words, the failure of Marx's predictions doesn't refute his laws since despite his occasional language he formulates no laws strictly speaking.
Eduard Bernstein realised that Marx's predictions were failing : Selected Writings of Eduard Bernstein, 1900–1921. Prometheus Books, 1996. Rosa Luxemburg in The Accumulation of Capital ( 1951) also could see that revisions were needed. George Lukacs's History and Class Consciousness ( 1971) rejected the idea of laws of development and recognised that Marx's trends could not support specific predictions, at least those that Marx had made. Finally in this brief survey Antonio Gramsci emphasised the need as he saw it for a political party, not a class-conscious proletarian class, to overturn the ideological hegemony of the capitalist class. Gramsci wrote in the wake of the rise of fascism in Italy; in a fascist prison he was sure that Marx had miscalculated the likelihood and power of proletarian class-consciousness and that the interventions of Mussolini's fascisti would block Marx's predictions, indeed had blocked them and would continue to do so until a communist party could emerge with the strength and determination to rival and overturn the fascist party. See Gramsci, Antonio, 1971, Selections from the Prison
Notebooks. New York: International Publishers.
A wider survey and longer list of Marx's social science predictions is offered in Fred M. Gottheil, Marx's Economic Predictions, Evanston : Northwestern University Press, 1966.