Depending on this detail, the character of this election process changes completely, since if repeats are allowed, it could easily degenerate into an oligarchy of ~50 people consistently choosing candidates from among their ranks.

"Electing the Doge of Venice: analysis of a 13th Century protocol"

Also some more discussion: https://news.ycombinator.com/item?id=38598171

https://en.wikipedia.org/wiki/Sortition

First, the development of the process: the system described came into effect in 1268, because previous systems had failed to satisfy fears of factionalism. IA bit earlier in 1229, a simple, one-round electoral council of 40 had stalemated, so lots were drawn, leading to a feud between the Dandolo family and the winner, Giacomo Tiepolo. Giacomo's son Lorenzo Tiepolo was the first elected under the 1268 system, which Nicolao Michele seems to have devised. Not mentioned in the article or discussions is the rule that the men selected were 30 years or older. [0] The violent factionalism and feuding preceding the new system, however, seems to indicate that oligarchs were fiercely competitive. The aristocrats were always going to choose some one aristocrat from their own ranks, but they were strongly divided against each other as well. I'm not sure there would be a solid faction of fifty or so to monopolize the process, especially given the random selections.

Secondly, those random selections by lottery, combined with the opening of the article ("an official went to pray in St. Mark’s Basilica, grabbed the first boy he could find in the piazza") points to another participant in this process, God. While today we tend to think of election protocols in terms of human actors, sortition can imply belief in divine providence taking a hand. The nomination and approval of candidates (election) at least nominally uses human estimation of merit as its input, while sortition gives divine knowledge of merit a role. The intertwined repetition of the two may have been thought to negotiate a best possible outcome from each set of inputs; in practice, against the backdrop of feuding and factionalism, it likely also made the ultimate 41 electors unpredictable and thus less prone to bribery or prior arrangements.

[0] https://origin-rh.web.fordham.edu/halsall/source/dogesvenice...

In computer age it’s long overdue to have a modern system with people directly voting for issues and causes and not represented by any middlemen.

That's absolutely bizarre. I'm sure if we had time to play it out a bit, there are ways to game that system easily enough, but it'd be really hard to see that from the outside.