The Decisive Fraction: What Percentage of the Population Wins or Loses a War?

In close elections, it's often pointed out (usually by the losing faction) that a relatively small portion of the country chose the whole country's fate, by choosing the country's next leader. For example, in the United States 2016 Presidential election, 42.3% of the total population of the country voted. But an even smaller fraction determines a country's future where the method used is state-organized mass violence rather than uncoerced choice. Here is a table of the most decisive battles of each war, and the fraction of the defenders' populations involved in each.

Battle	War	Year Fought	% Host Country Population
Hastings	Norman Conquest	1066	0.41
Spanish Armada	Spanish Invasion of England	1588	0.43-0.51
Plains of Abraham	Seven Years War (in North America)	1759	0.29
Yorktown	American Revolution	1781	0.41
Gettysburg	American Civil War	1863	0.40
D-Day	World War II	1944	0.40

Cherry picking? I chose the the most decisive battle in six conflicts in Anglophone history. Notably, the major decision I had to make was, for D-Day, do I use the combined population of the Allies (in which case the percentage is 0.063%) or, as I did here since it seemed to make more sense, the defending country hosting the battle, which was France. (Only a minority of troops in that battle was French.)

Is it possible that the most decisive battle is usually the biggest battle? Yes, I would think there aren't many most-decisive battles that are small - in fact the Battle of Plains of Abraham is famous for being small and quick among important battles. Looking at the Wiki article for the list of American Civil War battles, and at all the battles listed as having "A" importance as considered by historians, the mean and median come out to 0.21% and 0.18% of the population, with a range of 0.0004% to 0.58%. Clearly Gettysburg was bigger than all but a few of even the important battles (all but 6 out of 42 others.) If you'd like to add up all the "B" battles to look for mean and median go ahead - at a glance, they are clearly smaller on average.

The biggest land battle in history in terms of number of combatants is probably the Soviet counteroffensive at Stalingrad, which saw 0.59% of the Soviet population participate in the battle. We might reasonably consider this an upper bound of the amount of a civilization that could participate in a battle. This is also considered by many historians the most important battle of the war.

It is also possible that historians, lacking counterfactuals, merely pick the largest battles of any war since they have objective numbers of participants and casualties. However the counterargument there is that if the generals at the time did not consider a battle important, they likely would not have contested it with a large number of troops, and there would have been no large battle.

Assuming we're converging to 0.4 for most of the critical battles, what determines this number? My guess is it's a function of percentage of willing able-bodied men, transportation, and "surface area" between combatants. These of course are all pre-ICBM numbers, and now that we're all combatants, when a nuclear conflict occurs, the numbers will all be orders of magnitude higher, though it's hard to imagine a family sleeping in their home as combatants.