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I think this is going to be a difficult question to give a concrete answer to. (For many reasons: data isn't public, growth is very lumpy)
Probably the best approximation I can think of would be betting volumes in equivalent events over time.
US Presidential elections matched volumes on Betfair (in £):
* 2008: ~15mm (Source)
* 2012: ~40mm (Source)
* 2016: ~200mm (Source)
* 2020: ~1700mm (~600mm pre-event which is possibly more relevant)
That's a ~40x over 12 years, or ~35%/year.
We'll get another data point after the French Election this year and I guess it would be interesting to look at some other comparable events. (UK General Elections).
Another place we could look at is volumes on PredictIt, although that's really just a proxy for number of markets. You could also look at volumes on Polymarket or one of the other crypto exchanges.
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This is a chart of PredictIt volumes for markets I can find data for. I assign the volume to either the last day it was open (if that data is available) otherwise the close date on the market definition.
This tells a similar story to Betfair on "2016 vs 2020" and also illustrates the point I was trying to make about this being a tricky question - almost a large fraction of the volumes are coming during a few key events.
I would love to see a graph of the total amount of money sloshing around in prediction markets in 2021, 2020, 2019, etc. stretching back as far as we have data. I'm wondering whether there is a trend and if so what the growth rate is. My Google-fu is failing me so I'm asking here in case anyone else knows.