They do something similar with equity trades. They get professionals and public entrants to select stocks and include a 'dartboard'. From my limited reading experience the dartboard rarely wins implying people do add value, but it would be interesting if someone could find a history (I didn't with a quick Google). In Australia one news paper includes an Astrologer which I find amusing.
With start-ups I think it would be too expensive an experiment to fund.
On October 7, 1998 the Journal presented the results of the 100th dartboard contest. So who won the most contests and by how much? The pros won 61 of the 100 contests versus the darts. That's better than the 50% that would be expected in an efficient market.
"From my limited reading experience the dartboard rarely wins implying people do add value"
This is wrong. If the dartboard consistently underperformed most stockpickers (i.e. say it ranked around the 30th percentile year over year) then you could make the case that (some) people add value. If, on the other hand, the dartboard is near the mean of the distribution of outcomes, you could make a case that it's all luck.
The fundamental fallacy underlying the "Darts are just as good as people" is that the _entire reason_ the dartboard approach is so successful is because of the massive number of experts who have priced everything close to perfectly.
No such market exists for startups - so selection is required.
You're right. The dartboard experiment would be better (faster) if you had just as many dartboards as investors. Then you could compare the distribution and not just a single result.
With start-ups I think it would be too expensive an experiment to fund.