Well, the formula isn’t entirely arbitrary. The effect is to score candidates by the geometric mean of their sum and average score. Thus, if summing and averaging agree on the order of two candidates, then this rule maintains that order (actually, that should probably be its own criterion, SUM_AVG_AGREEMENT). When summing and averaging disagree, then the ordering of the method with the more lopsided ratio wins out. As averages are bounded but sums are not, there’s more room for a lopsided ratio of sums than a lopsided ratio of averages, so sum is probably going to overrule average more often than the reverse, making this quorum rule rather aggressive. However, this may not be a bad thing - whether or not the average of a large number of scores (say, a million) coming from an even larger population (say, a hundred million) is trustworthy, anyone who wins like that will have issues appearing legitimate.
One thing to very much dislike about this rule is that while average scores and sums of scores have plain meaning, there’s no obvious way to express this without math. Even an ‘automatic zeroes’ rule can at least be described as a pessimistic estimate of what a candidate’s average would be if they were more widely known.
It does indeed fail participation, although the margins have to be very thin.
For example, in a 0-5 score election, if Candidate A has sum of 115 on 30 ballots for an average of 3.833, and thus a score of 20.996, and Candidate B has a sum of 210 on 99 ballots for an average of 2.121 and thus a score of 21.106, then if the next voter gives B a score of 5, A needs to be scored at least 4.707 to overtake B.