Hello  Dave and All,
The subject of more than one queen in a hive has came up hundreds of times in meetings I have attended through the years. . Many noted researchers have commented on the subject. I will list a few of their comments.
Most researchers say beekeepers simply open a hive and find two queens and assume many things about the situation.
Researchers explained to us at these talks  that something is wrong with the genetic makeup of bees which allow two queens OR there is a very simple answer which the observing beekeeper is not seeing such as.
1. The bees have raised a new queen and the two have not met yet.
When I have found two queens in the same hive there have been an old queen and a young queen. When I took the two and put together the battle was on. Maybe Dave has tried putting the two together and will comment. I DO NOT leave two such queens in a hive because it serves no purpose for me. I leave the younger of the two.
2.Researchers explained that beekeepers which keep bees in three or more deep brood boxes frequently find two brood nests if there are two entrances such as one at the top and one at the bottom. Put together alone the two queens will start fighting even though they have got the same hive odor. 
In my two queen colonies when I pull the excluder to combine after about two weeks into the main honey flow at times the two separate queens will continue as two queens for longer than I would like but eventually the worker bees returning through the bottom nest will kill the lower queen. I can always tell these hives in which both queens laid past the time I wanted after I pull the supers by the amount of brood in their before combined positions.  100,000 bees in the hive at the end of a honey flow are not a good situation. for me.  Properly combined two queen hives are combined so the hive population of a two separate brood nests combined is about the same as a single queen population AT THE END OF THE HONEY FLOW.
A cruel method I have seen practiced by commercial beekeepers is to pull honey supers *bees and all* and let the bees fly out over the 100 miles back to the extracting plant. The purpose is to reduce the bee population sitting around eating up honey needed to winter on. Young bees winter better than old bees. 
2. small after swarms will at times enter weak hives and set up housekeeping. When I put the queens of these together they always fought.
3. . The most popular reason other than the above which is a simple logical explanation is genetics.
A genetic pheromone problem. Both queens are giving out LOW levels of pheromones  The researchers explained that with both giving out low pheromone levels the bees did not see the two queens as a problem. Bees will ball an old queen most of the time when a supercede young queen returns and they notice how weak the pheromones of the old queen are. We really do not know everything about queen bee pheromones but we do know the pheromones get weaker as the queen ages and supercedure will start at a certain point. We also know queens of over several years old have had strong enough pheromones to prevent supercedure while young queen of only a couple months have been superceded by the bees for low pheromone output.
Dave wrote:
Certainly among the colonies that I have kept during the last 20 years it has occured in about 75% of them.
This seems like a rather high figure and would lead me to suspect a genetic problem. Please do not get upset Dave as only my opinion and I am wrong at times.  As a honey producer I see no valid reason for leaving two queens in the same hive except for a specific reason such as brood production before a honey flow. If those were my hives I would requeen all those A.m.m. hives with an Italian strain. Dave and I have been friends for a long time Bee-L listers so we kid back and forth about the merits of A.mm and Aml. To sum my post up all the researchers in all the talks say there is a perfectly logical reason why two queens might co exist in a hive if the problem is looked at close enough. Maybe Dave and Dee do not see multiple queens as a problem but I see the need for two queens only for the reasons I stated. 
A curious situation which Dave talked about in great detail on the Irish list was finding his numbered queens  from one nuc in another nuc and the numbered queen from that nuc in the other nuc. I honestly have not got an answer for that situation unless his bee buddies are playing tricks on Dave. Comments/
Sincerely,
Bob Harrison
Odessa, Missouri