A burka ban is excessive relative to its object
The burka is worn by less than 1% of Muslim women. A blanket ban is not a proportional response in relation to the object.
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Between 0.01% and 0.04% of all Muslims choose to wear a burka. This makes up a microscopic proportion of the British population. This puts the total number of wearers in the UK at between 3,000 and 5,000.
When considering whether or not to impose restrictive legislature, the government has the responsibility to consider whether the measure is proportional to the objective. For example, the UK government has often discussed the introduction of citizen ID cards, like many of its European neighbours. These ID cards, which citizens would have to have on them at all times, would theoretically make the country safer by allowing police to instantly identify any citizen in any public space. The UK public has rejected any attempts to introduce the cards. While the cards would undoubtedly make the country safer and improve national security, the measure is not in proportion to its aims. The benefits earned would not outweigh the sacrifices the public would have to make to their individual freedoms. The burka represents the same unequal trade. Given the number of women actually wearing a burka is so small, the ban is not proportionate to the "threat". It does not warrant so much time, effort, money and public energy. There is not even much to be gained. Would a burka ban lead to significantly more gender equality? Almost certainly not. The scant evidence for banning the burka on the grounds of national security also suggest that it would not make the country a vastly safer place.
There Is no Trade-off In the example described, the trade-off under consideration was the desire to increase national security against the freedom to walk around without an ID card in your possession at all times. There was a clear trade-off between civil freedom and improved security. However, in the instance of a burka ban, there is no trade-off. Women that previously wore the burka are free to wear the chador, niqab or hijab. They would not lose any of their religious freedom. Also, the fact that so few women wear the burka means that any sacrifices are very small. If banning the burka provides even a modest increase to public safety, it should be employed because the disruption would only affect a tiny proportion of the population. On the other hand, there is potentially much to be gained in the areas of gender equality and national security.
[P1] So few women wear the burka that a ban is a waste of public time and effort. [P2] Therefore, it should not be undertaken.
Rejecting the premises
[Rejecting P1] In a cost-benefit analysis, because so few women wear the burka, a ban would be minimally disruptive but could have substantial benefits. Therefore, a ban should be enacted.