If this is truly the reason for the lotteries, is the government / tax agency giving out the prizes? I never bothered to look closely but it always seemed something run by those businesses.
Yes of course. Every country has trouble collecting taxes. In Taiwan they memorialize the day when the police were too heavy handed with a woman selling untaxed cigarettes. A citizen died in the skirmish.
This day is 2/28 and largely remembered as the beginning of a 40 year period of martial law in Taiwan. I recommend visiting the 228 museum in Taipei's peace park. Even though the current government, KMT, revised the history in this museum to downplay the fact that 20,000 people went missing in Taiwan during this period, the museum still tells a great story. It's great because the story wouldn't exist at all in a place without free speech, such as China.
Though as I understand it, it requires a dot matrix printer to populate these receipts (or writing them by hand).
Edit: reading further I see China is rolling out their lottery in more areas the last few years
We asked for them quite often and they gave them each time. Total, we won 2 cans of Coke and maybe 10 yuan :)
Fun fact - fapiaos you get might be fake. Once I got fake fapiao, printed from fake printer, in fake taxi. I know it's fake because I tried to validate it online (there's service for that) after I noticed I got fake bill :/
One thing I wonder is if you have an increased likelihood of winning if you buy more. Does a $1 purchase give you the same chance to win $100 as a $20 purchase? I don't really know. Over 100 receipts you usually win like $5
Also, people here know they can report a business for not giving out receipts. They might get a share of recovered taxes for that.
I don't know all the pros and cons of that setup but it seems there are ways to maintain a cash based system and still collect taxes.