The other day, someone who I respect greatly posted something that has started a bit of a debate (as much as debate can be had on social media, anyway). Omer Bor posted his views about the planned change in the bus fare cap in England to £2. His views in short are there are probably better uses for half a billion pounds than a simple nationwide flat fare, which caused a bit of discussion in the comments section of that and one subsequent post - including from yours truly.
Rather than rehash the debate again but in longer form, I thought what would be more useful ns looking at the different pricing mechanisms, and their relative strengths and weaknesses from the perspective of modal shift, equity, and economic efficiency. Each of which is usually contained in the vision and objectives of the transport strategies that such fares are meant to help deliver1.
I also do this partly as I find that people weirdly get really protective about their own chosen method of pricing public transport. Seeing panellists at a conference get quite angry that someone disagrees that free public transport might actually not be a good thing is quite something, I assure you. But hopefully here you may be able to learn something about the value of each method of pricing.