Who would win the war if wizarding England fought against Muggle England?
I once got into an argument with a friend of mine as to who would win an all out war between the wizarding community and a muggle population that was fully aware of its presence (if not it's location) and in a genocidal mood. He seemed to think that magic would put the muggles at an extreme disadvantage.
This is of course, utter rubbish.
My reasons for this are;
From what we know of the children population at Hogwarts, there are several factors indicating that the numeric superiority belongs to the Muggles. For example, there are only six male Gryffindors in the same class year at Hogwarts. Nowhere does it suggest in the Harry Potter series that this is abnormal. If we can assume that the female equivalent of Harry's year is the same, and that Harry's class year isn't smaller or larger than normal, then we have around 70 Gryffindors altogether. All indications are that the children are then spread evenly amongst the four Houses, which would then give us 280 students all together. Hogwarts is known to be the only school in the UK, and there is no mention of homeschooling, which indicates that if it does exist in the UK, it is very rare. Additionally, there is no mention of there being a "baby boom" or any major "empty" generations of low population, so this is likely not to be an unusual number of students to attend Hogwarts.
We can likely assume that the First Wizarding War caused sufficient casualties to reduce the Magical population sufficiently enough so that school attendance has drastically fallen for at least a decade. However, the problem with this theory is that it would mean that everybody from a magical family would have had to have lost at least one family member for this to be the case.
The Second Wizarding war was marked by an aversion to mass casualties amongst the wizarding population, with only skirmishes and assassinations (Madam Bones). It is more likely that Voldemort would've used then intimidation, coercion and the use of the Imperius curse to enforce his rule upon others. It can be safely said, therefore, that the student population of Hogwarts during Harry's school years is largely representative in numbers. Therefore, if you take into account the numbers of students at Hogwarts, and the underage magical children aged between 0-11 years old, there are only around 700 individuals, which includes the Muggle-borns as well.
Using rough math, I then arrived at a portion of there being 5 ½ of adults for every student. However, I have not taken into account any demographic perculiarities, so for generosity's sake; there are probably around 7 adults all together, for no other reason than 7 being a magical number. Even so, this means there are less than 5,000 witches and wizards in England.
All together, there are 60 million muggles who live in the UK. This means that it is likely that no more than 0.00083% of Britons have any magical ability whatsoever.
Military forces and weaponary
From what we have seen of the forces of Wizarding England, there are only hitwizards and Aurors used by the Ministry of Magic. At no point has there been any mention of a standing army for the Wizarding world. This means that the wizarding world relies on its police to keep order in the wizarding world. While this can probably be expected due to the low population of Wizarding England, it still puts it at a severe disadvantage against England's Muggle army. The probable reason for the lack of any military forces is because the main job of the Ministry of Magic is to keep the Wizarding world hidden from the Muggle world. It would be pretty hard to hide yourselves should you go to war with another wizarding government.
In addition, the weapons of the Auror are severely limited, but effective. With only one weapon (a wand) but with an unlimited use of spells, the average Auror should be able to deal with an attack. However, from what we have seen on the physical activities at school, there is very little exercise. Added with a general disdain of Muggles, it remains highly unlikely that they would use hand to hand fighting, meaning that if they were separated from their wand, they wouldn't be able to fight well. A Muggle soldier often trains in hand-to-hand fighting in case he loses his weapon. If it came down to it, the Muggle would almost certainly win every time.
The real problem, however, with wizards and wands is that it is highly emphasized that the best way to win a battle is through non-verbal spells or wandless magic. For the latter, there has only been limited evidence that it exists, and probably is used by Lord Voldemort or Albus Dumbledore. Other lesser examples of wandless magic can be seen in the Order of the Phoenix, when Harry successfully managed to light up his wand by saying "Lumos". However, whether this was a successful attempt at wandless magic or accidental magic brought on by stress and fear is debatable. As for non-verbal spells, it is more likely that the more-than-average wizard is able to accomplish this. However, for the most part, it remains likely that wizards rely on verbal-spells. The problem with this is that Muggles don't need to use verbal words, but can rely upon guns.
Guns against a wand will probably be a matter of whether the wizard is or isn't aware of his opponent. Should he be fully aware, and be able to cast a shield successfully, it should be able to hold off bullets. Our evidence for this can be seen in the film, the Order of the Phoenix, during the fight scene between Dumbledore and Voldemort. Voldemort had just fired huge amounts of glass at Dumbledore, causing Dumbledore to raise a shield. The glass passed through the shield, but had been turned into dust that was harmless. However, should a wizard be caught unawares, then the bullet will penetrate and wound/kill the wizard.
Should a sniper be used, then there really is no contest there. Again, if the wizard is unaware of the sniper, then he will be shot down from afar. One of the best sniper rifles, the 50 BMG has been known to have killed a person at a range of 1.5 miles. Compared to a spell which depends upon accuracy at close range, there is very little a wizard can do against this.
Finally, we go onto the methods of mass-destruction that Muggles have developed. There appears to have been little thought whatsoever for the capabilities of Muggle weapons, such as Nuclear Weaspons, gas, shrapnel, napalm or even a landmine. It is often described by Purebloods that Muggles are worthless and pointless; therefore, it is highly unlikely that any thoughts would be put onto creating any wards or weapons to counter these weapons.
Wizarding England, as a whole, has shown itself to be careless and shown little concern towards Muggles. In a war against Muggles, it would be incredibly difficult for
Wards and escape
The problem with trying to fight a war with wizards is that they have developed the ability to teleport into places. One of the most powerful wizards, Dumbledore, was shown to have apparated at least halfway across of England from Hogsmeade. Whether an ordinary wizard is able to do that is debateable. Either way, the problem with fighting a war against wizards is that they are so damn flexible! They will have the advantage of manoeuvrability in a war, getting past defences, blockades and roadblocks. They will be able to use hit-and-run tactics against individual targets before escaping again.
Another problem with fighting wizards is that they have developed anti-Muggle wards, which pushes them away from a target. Another problem is the fidellous charm or the unplottable charm. This would make finding a target virtually impossible. Of course, there is a way around everything. The problem with wards is that while they may affect Muggles, it doesn't seem to have any effect against Muggle satellites. Another way of finding a building hidden by wards is to use infrared to discover where they are.However, should that target building be free of wards, then it is going to be likely destroyed quickly and efficiently. A bomber, a missile or even a tank would be able to destroy the target building. A tank would most likely suffice because of its amour. There is no spell mentioned that would be able to destroy a tank, with only one spell,Confringo, which was used to destroy the side of the flying motorbike in the Deathly Hallows. Used against a tank with superior armour that would be able to withstand against explosions, very little would be able to destroy it.
Owing to the small population of wizarding England, it is very unlikely that there are any farmers used by the wizarding population of England. This means that they likely get their food sources from the Muggles. Farms wouldn't be in general use in the wizarding world, mainly because they wouldn't be able to get the manpower for it. If they tried to use, for example, House Elves, the problem with this is that they have been shown to be limited in number, with normally only a few in the service of Pureblood houses and to Hogwarts. This means that they wouldn't be likely used for this. If war was declared, then the Muggles would attempt to stop any food supplies from coming in. While this will probably always be inefficient, it will still cause for a shortage in certain types of food.
The problem of the Imperius curse
One of the biggest problems that Muggles would face is that their leaders and general are susceptible to being placed under the control of wizards. Without an efficient leadership, it is difficult to see how a war against Wizards could be fought. There is very little way to prove that they are under the Imperius curse either way. Anyone could point at a person whose acting differently to how they sometimes act, and claim that they are under the curse.
One of the largest difficulties that wizarding Britain would face is the good relations that Muggle Britain has with the rest of the Muggle world. Whether the Ministry of Magic has a good relation with the other governments, it is not certain, but if you take into the account the probable low population of the wizarding world, then there is very little that can be done for the wizard world internationally. There may be isolated cases of foreign wizards helping the British wizards, but it would be very little. On the other hand, the UN and the EU would probably send soldiers to assist Britain if it was at war with the wizards. They would also assist by sending better weapons and soldiers to assist in putting down the wizards.
A large problem for Muggles is that a lot of animals in the wizarding world are invisible, such as Dementors. The only way that a Muggle can know if a Dementor is there is through the intense cold that is given off by them. There are also many other instances of other dangerous animals, such as giants, Hagrid's favourite creatures (Blast-ended Newts) and of course, the Dementors. Whether only a few of them are invisible isn't known, but the real danger does lie with the Dementors. It is hard to kill an enemy you can't see.
From what we have seen of wizarding England, it has very little compared to the Muggle world. Wizarding England appears to have adopted a policy of "Magic can do anything". This has resulted in very little technological advances, perhaps due to magic interference with electricity. Either way, the Wizarding England is still using feather-quills when Muggle England uses biros. Old fashioned clothing (robes) are still being worn, when trousers and t-shirts are the norm for average Muggles.
In conclusion, in a war between muggles and wizards, it would be extremely hard. The advantages of the Muggles and Wizards follow as:
Therefore, I leave it up to you to what you believe. I would also like to give a really big thanks to veritaserum in the debate whether the Muggles could or could not win against the Wizards. A great deal of information was gained from the debates going on, and I hope to read more of it another time.