Social choice theory can be powerful tool for analyzing voting power.
In a poker game, if one player has a pair of twos and the other a pair of kings, who is more likely to win? Travis Dirks, managing partner of Rotary Gallop, argues that the fact that kings are worth more than twos won’t necessarily determine the outcome of the
hand; what really matters is the number of different ways in which the player with a pair of twos can get another two, given the cards remaining in the deck.
The poker example directly relates to how corporate secretaries might look at a pending proxy contest. By counting cards – or modeling all the various voting scenarios – companies can get a more accurate handle on which shareholder
proposals to fear and which to shrug off.
Dirks grew interested in looking at shareholder voting through the lens of social choice theory, a framework commonly used for considering how the political map might look under various scenarios. ‘In politics, your influence over the votes is the thing we
really obsess about,’ he says. But social choice theory is particularly interesting for corporate democracy, given that shareholders each hold different numbers of votes, and these voting blocks can be cast only one way.
‘What voting power tells you is, out of all possible outcomes, in how many of them a particular shareholder
gets to decide the result of the vote,’ says Dirks, a physicist who has converted a hobby investing in equities into a
business. His partners, Radhika Rangarajan and Guy Tal, have doctorates in quantum physics and mathematics, respectively.
Ron Schneider, senior vice president at Phoenix Advisory Partners in New York, notes that proxy advisers are always seeking novel ways to sharpen their projections. ‘With the stakes higher than ever, including majority voting, director withholds have real teeth,’ he says. ‘Given how close many votes are, companies want the best intelligence they can have on what outcomes they can expect
before they make key decisions.’
Working through the math
Most proxy solicitors today categorize shareholders as ‘for’ a measure, ‘against’ it, or ‘undecided’. They then weight the undecided voters according to the number of shares they own before trying to influence the swing voters.
‘That gets you a lot of the way there,’ acknowledges Dirks. But it doesn’t tell you the relative importance of
the names on the undecided list. If, for instance, shareholder A and shareholder B both own 49 percent of the shares, and shareholder C owns just 2 percent, what is each shareholder’s relative influence? In fact, all three have exactly the same influence, because any one of them might serve as the swing vote. This leads Rotary Gallop to what it describes as Rule 1 of voting power
analysis: ‘A voter can have drastically more or less voting power than his/her ownership would indicate.’ The concept of calculating influence is fairly straightforward – the complexity arises when the numbers grow and the possible options keep branching off. ‘The
difficulty comes in the fact that each time you add a voter, the number of possibilities for how the vote can come out doubles,’ says Dirks. ‘So when you get to 100 or 1,000 shareholders, it’s computationally challenging.’
Rangarajan points out that companies and activists have ‘relied on intuition and back-of-the-envelope-type calculations – nothing quite as rigorous as what we can do for them.’ Cary Klafter, corporate secretary at Intel, believes voting power analysis might prove very relevant for some proxy situations – and virtually irrelevant for others. ‘In most situations the vote isn’t close, so the issue won’t come up,’ he explains. ‘In many companies, however, the voting power is very diffuse. In these cases you have to go pretty far up your list to the very substantial investors to reach the people who really might be swing voters.’
Klafter suggests that the value of the model will differ greatly by company and circumstance. ‘If you have hundreds of investors who each own one third of 1 percent, it’s a very different case from when you have a few investors who own 3 percent, 4 percent or 7 percent,’ he explains.
Practical applications
Voting power analysis is already commonly used in politics, especially in the European Union (EU), where the influence each country should wield in reaching decisions is hotly debated. Rangarajan notes that in the 1960s there was uproar when Luxembourg, with a population of only 310,000, was given one vote in the Council of the European Economic Community, while larger countries like Germany or France shared their votes among many more citizens. West Germany (as it was then), for example, had one vote for every 13,572,500 people. Thus, a citizen of Luxembourg appeared to be roughly 44 times more powerful than a German.
‘When you do the math, there was no reason for the uproar because Luxembourg had zero voting power,’ says Rangarajan. In other words, its single vote would in no conceivable instance prove decisive. ‘Since then the EU has done quite a bit to incorporate these kinds of analyses into its politics,’ Rangarajan adds.
On the proxy front, Dirks points out that voting power analysis can help corporate secretaries identify up front when the odds are skewed such that there’s little chance an activist will prevail. In instances like this, he says, the company can feel confident in going ahead with the proxy battle. In less clear-cut cases, the model helps corporate secretaries decide which investors should receivethe most time and effort – or the most concentrated lobbying blitz – in order to achieve the company’s goals.
Naturally, a tool for more accurately predicting outcomes in proxy votes would be extremely powerful for corporate secretaries and activists alike. Mike Levin, founder of website The Activist Investor, says that what Dirks has systematized is something he and others have long sensed intuitively. ‘Not everyone does this type of analysis, because it takes some doing to figure out who’s
in a position of influence rather than merely adding up the votes,’ he says. ‘But smart people do it.’
Levin notes that with the loss of the broker discretionary vote (NYSE Rule 452) and the changing landscape of the investment scene – which now includes far more hedge funds – the need to calculate odds and better understand influence has grown. ‘Management
used to exert a lot of control over an election,’ he points out. ‘It really didn’t matter who could be influenced, because management held a lot of the votes. That’s all changed now.’
Klafter raises a similar point. ‘Corporate secretaries are quite cognizant of the fact that with the NYSE rule having been amended and pretty much on its way out, you have a shift of voting patterns that favors the institutional investors,’ he explains. ‘Institutions are simply going to be there and vote, and if you have majority voting for directors, institutions will have a more effective voice
because they always vote while other folks might not.’
‘The corporate mind set has changed,’ concludes Schneider. ‘Companies know the stakes are high. They don’t want to lose by 1 percent and then have to answer to senior management.’
