For me, I'd start out with the widely accepted definition of the term Sixth Man and their role in basketball:
Wikipedia wrote:The sixth man in basketball is a player who is not a starter but comes off the bench much more often than other reserves, often being the first player to be substituted in. The sixth man often plays minutes equal to or exceeding some of the starters and posts similar statistics.
NBA.com's Hoopedia wrote:The NBA Sixth Man of the Year Award is the award given by the National Basketball Association to the league's most valuable player for his team coming off the bench as a substitute (sixth man). To be eligible for the award, a player must come in off of the bench in more games than he starts.
I think it would be fair to define a sixth man as a reserve player who sees significant minutes and is arguably the best player coming off the bench (certainly the bench player with the best statistics). To further define the characteristics and role of a sixth man, I would say that sixth men are players who are better suited to coming off the bench either personally or strategically, are prime candidates to take the place of a regular starter when needed (and could perhaps be a regular starter on another team in the league) and provide their teams a capable and productive player in a reserve role, generally being the first substitute to enter for their team.
In that regard, I don't think you can disqualify players because they are arguably better choices to start regularly, start some games during the season or play a lot of minutes, comparable to (or more than) one of the regular starters as they're still being utilised in the traditional sixth man role. You do have to invoke some limit on the amount of games started and less than half seems fair enough. Perhaps bringing that number down to 30% (ie no more than 25 games assuming a player appears in all 82 regular season games) would fairly eliminate those who are on the border of being sixth men and frequent starters.
From there, the statistical production of each qualified candidate could be analysed and compared to decide the league's best reserve player. If the Sixth Man award is to be considered the MVP of reserve players as defined in NBA.com's Hoopedia, team records and production when the Sixth Man candidate is on the floor would also presumably come into play.
So I guess my criteria would basically come down to potential candidates satisfying the requirements for percentage of games started and being the most prominent reserve on their team, thus fulfilling the traditional role of sixth man by being the most productive/talented player coming off the bench for considerable minutes because it is a role they are better suited to or because it offers a strategical advantage.
The criteria for selecting a winner from the qualified candidates would then simply be a comparison of each player's performance with conclusions drawn on each player's importance to his team, with the award going to the player with the most impressive results.