Well what figures to the left of kerensky might have been chosen either first for war minister or later picked for PM?
Chernov would be the obvious candidate for Prime Minister in a non-Bolshevik soviet government. The problem is that the Mensheviks, due to their dogmatic Marxism, felt that the Russian revolution was still going through tis "bourgeois" stage, and that too left-wing a government (which would mean a break with the Kadets) was therefore not desirable. And alas the SR's went along with the Mensheviks on that point. To quote an old soc.history.what-if post of mine:
"As it was, the Mensheviks and SRs were handicapped by the fact that in
each case the right wing of the party was dominant, and the left wing did
not want to split with it (except, as I noted, some of the extreme left-
wing SRs, and even they split only after October). The Right Mensheviks
and Right SRs opposed an all-socialist government and insisted on
supporting Kerensky (himself nominally an SR though he regarded himself as
being above parties) and on maintaining a coalition with the Kadets. In
the case of the Right Mensheviks, this was due to a dogmatic Marxism (the
Mensheviks were always more "orthodox" about their Marxism than the
Bolsheviks): Since by all orthodox Marxist standards, backward Russia was
not ready for socialism, it was essential not to alienate the bourgeoisie
from the revolution. As for the SRs, they were curiously willing to
follow the pro-war, pro-coalition-with-the-Kadets Mensheviks. Oliver
Radkey in *The Agrarian Foes of Bolshevism: Promise and Default of the
Russian Socialist Revolutionaries, February to October 1917* (New York and
London: Columbia UP 1958) notes that the Mensheviks' concept of
revolution was "as though made to order" for the right SR's, "whose zeal
for war led them above all else to desire a class truce, which could only
mean the bourgeois hegemony of the revolution postulated in Menshevik
theory" (p.467). But Radkey also adds (pp. 466-7):
"'Yet it was not just the right wing which held the PSR in thralldom to
Menshevism. The center was also responsible for this fateful dependency of
the larger party upon the smaller, even to the extent of abandoning its
own concept of the revolution. Chernov says the SR's were twice late in
respect to coalition, first with its formation, and then with its
liquidation. But he also tells us, on an earlier occasion when the
impression of the overwhelming catastrophe sustained by his party was
fresh on his mind, that at the time of the July crisis the question of a
socialist government had been posed and had been decided in the negative,
partly because the Mensheviks refused to join. A break with Menshevism was
by no means desired by many adherents of the center, leftist in
inclination. Presumably he numbered himself among these members--he was
always friendly to Menshevism. It was at the Tenth Petersburg Conference,
however, that he spoke more frankly than on other occasions. He admitted
that SR tactics had been framed with reference to Menshevik tactics--
sometimes excessively so. He admitted that for the Mensheviks, with their
concept of a bourgeois revolution, coalition had been a goal, whereas for
the SR's it was only a means. When Tsereteli at the Democratic Conference
termed 1905 a failure but this revolution a success, because of the
achievement of coalition, Chernov had realized that their paths were
fatefully diverging. Need he have waited so long? And why, after the
truth finally dawned upon him, should he have thought of Tsereteli as
minister of foreign affairs in a government headed by himself?'"
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