I very much question your assumptions about how a smaller number of votes would work. The total vote weight would fall dramatically and people with a lot of stake, despite fewer votes, would then still have enormous influence over the now-lower weight totals. 

Consider the extreme case of only one vote. I'm reasonably certain that every single top witness in that system would still have at least one very large stakeholder vote supporting them, including some large stakeholders who would split their account in order to have more flexibility in voting. It is even quite possible that some large stakeholders, or possibly all of them, would be able to place one or more witnesses into the top list with their votes alone. That is bad, not good.

It is far from clear to me that more votes favors larger stakeholders in any significant way; everyone simply has the same increased opportunity to express support for more candidates, including smaller stakeholders doing so. For example, with only a few votes, as a smaller stakeholder if your first few choices have no real chance of being voted in, then you have to choose abandoning them to have immediate influence between candidates all of whom you may dislike but are credible current candiates. With more votes you can continue to support your first choices (who may then gain additional support over time) and _also_ have immediate influence on the margin. That is the sort of strategic gaming that approval voting aims to (and largely does) eliminate.

There is no way to avoid someone with a million (or even a thousand) times more stake having enormously more influence, and if you could that would be bad because it would mean that an attacker will less stake would therefore gain more influence. 

At a minimum, this proposal would require a far stronger argument than what you are making that it would have the beneficial effects you suggest (like an actual paper, with proofs, which considers among other things, strategies like account splitting). 

In the absence of that, the baseline assumption I'm going with is that approval voting with unlimited (or at a minimum least >20 votes) is best here in order to get witnesses that are 'acceptable' to the largest amount of stake (which is both a desirable governance and security property)

BTW, remember, most of the largest stakeholders currently vote for more than 20 candidates (most vote for close to 30 and ideally the limit would be higher). It is then the smaller stakeholders who decide among the candidates who are acceptable to the larger stakeholders (and also vice-versa, because there is no inherent ordering to the votes, but this may be less clear to you without really thinking it through).

Again, yes, the largest have the most influence (and when the disparity in stake is very large, the disparity in influence is as well), but all votes absolutely do count.

> As a counter example, if one malicious group were to acquire enough stake they could vote in all of the top 20 witnesses themselves, yes it would require a big stake, but it could be done in theory, they could vote in all 20 of "their" people

Under your proposal this would still be the case, they would just need to split their stake into 4 or 5 accounts. The total vote weights necessary to get in the top 20 would fall dramatically, so the total stake required would correspondingly fall.