Recently I have read an article that claimed that Stalin wanted to introduce competitive, alternative elections in the USSR while the regional secretaries were strongly against the idea and pushed for a "great purge" of 1937 so to secure the positions after the new constitution of 1936 was introduced.
Some background. Following the constitution of 1926 the deputies were elected by the working collectives rather than by a popular vote. This was done so the the bourgeoisie could not participate.
The "stalinist" constitution of 1936 was the first to introduce the voting principle similar to the capitalist countries: the deputies were to be elected based on territorial principle. The newspapers of the time described the forthcoming voting as alternative and Stalin himself made a speech underlining the importance of the possibility of "revoking" a deputy, which as he claimed, was absent from the law of capitalist countries which made the deputies completely independent from the voters during their term.
The article claims that the secretaries were very much in fear about them to loose elections and pushed for political purges which they hoped to control.
Note also that Stalin was behind many other ideas that made the USSR more like other capitalist countries: he pushed for re-introducing military ranks, scientific degrees, reconciliation with the church, abandoned the idea of the world revolution, disbanded Comintern, renamed Red Army into Soviet Army, substituted the political commissars in the army to the commanders.