But if the assumed level of take-up is wrong...?
For example, from Batley to Mirfield I won't always get ticket-checked. If I do, the guard looks at the card for less than a second, acknowledges me and moves on to the next person- that's the nature of the job at present... but how is the fact that I've been on that train and used an MCard actually recorded officially? Do the new (guards') ticket machines allow the guard to log on the machine, that a PTE ticket is used? Or, as I suspect, am I invisible as far as ridership figures are concerned?
It's only anecdotal admittedly, but I'd have guessed that MCard use on the Huddersfield to Leeds axis is closer to 20% than 10%, though a fair bit of that may be the StudentPlus MCard which is probably wise to record separately.
As
JCollins says all you need is a representative sample of a minimum size that is readily calculated, certainly not to count every journey.
Probably not a good example, given their prediction record, but a representative sample of around 5,000 people should be enough for a poll to predict an election result within 1%. The problem opinion polls have is finding a representative sample with wild swings of turnout by different demographic populations over recent elections. Exit polls have suffered less from this problem, because they actual ask people who have voted, but the remarkably accurate exit polls at the last election were based on asking 100 voters at each of 100 polling stations how they voted, not asking all 30m voters.
Just as your journey is invisible, the fact that votes of 30m voters were invisible to the exit pollsters is neither here or there.
Are you really claiming that the measured level of takeup is wrong based on one person's anecdotal evidence based on a single flow? What sample size does that represent and what evidence do you have that its representative? Sorry but it would be hard to think of an better example of an unrepresentative sample based on an inadequate sample size, virtually guaranteed to give wildly inaccurate results.