You're asking an intriguing question. I agree with the comments that are showing some apprehension at the "one-man-one-vote" system. I also agree that knowing the basic statistics (like standard deviation and mean) will not give you an insight into the will of the voters.
I would like to play off of David James's answer, keying in on stakeholders. Instead of a vote, perhaps you could give stakeholders a virtual account, which they must "spend" on the candidates.
If they had
$100 each, then perhaps one stakeholder would show a strong preference for candidate A by spending all
$100 on him or her. Another stakeholder might like candidate B slightly more than candidate A and spend
$60/$40. A third stakeholder might find all three candidates equally (un)appealing and spend
A variation would be to give different stakeholders accounts of different sizes. For example, perhaps the exiting CEO gets
$200 and a worker's representative gets
You could even ask for an open vote, where each stakeholder explains his reasoning.
Highest earner wins the position. Or maybe the top two get the most careful look and a runoff.
This betting technique is an adaptation of what is done in Blind Man's Bluff: The Untold Story of American Submarine Espionage (1998, S. Sontag and C.Drew) A B-52 bomber collided with an air tanker, and they lost an H-bomb.
Craven asked a group of submarine and salvage experts to place Las-Vegas-style bets on the probability of each of the different scenarios that might describe the bomb's loss.... Each scenario left the weapon in a different location.... He was relying on Bayes' theorem of subjective probability. (pp. 58-59)
Whatever you choose, please make sure that the rules are clear before you start voting on candidates. A perception that the rules changed will not help the transition.