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Summary:

• I don't see how it's more private than publishing income?
• I don't see how knowledge of gross and taxable income allow to deduce tax fraud?
• I'm afraid publishing this information will not help in terms of tax fraud but possibly hurt general society "climate".

Privacy compared to publishing income

published the percentage rate of tax that each citizen paid?

i.e. taking the gross income before deductions and the tax paid and turning that in to a percentage.

Do you mean publish = make available to 3rd parties or tell the citizen what their effective tax rate is?

The latter is done in Germany: the income tax statement has an information line that states average tax rate as percentage of taxable income (not before deductions). However, I'll assume you're talking about the first meaning.

In case you mean publishing to 3rd party, I don't really see where the big difference between publishing taxable income vs. publishing effective tax rate is in terms of privacy?

Here in Germany, the effective tax rate is a strictly monotonous function of taxable income (https://de.wikipedia.org/wiki/Einkommensteuer_(Deutschland)#/media/File:ESt_D_Splitting_2018_zvE_bis_120000.svg), with 2 exceptions:

• taxable income so small that it is in the 0 tax zone and
• capital gains are mostly handled separately from other types of income, and with a constant tax rate, so for that part, you cannot conclude much from the tax rate.
  (There are again exceptions from the exception ... here it's getting quite complicated, because also the company where the capital is invested pays something like income tax before dividends are paid out...)

Personally, I'm very much in favor of privacy rights (along the line that I behave well and in concequence expect privacy), and in my culture personal income and/or wealth are considered private. From that perspective, I do see a huge difference between a (or few) tax officer(s) who took an oath that they will obey all laws and will be scrupulously correct in administering their duties knowing details of my financial situation in order to calculate my taxes and random persons getting this knowledge. (more below in section "Does it help")

Does it help detecting tax fraud?

It strikes me that this approach would help to highlight tax avoidance without giving away too much personal information.

I don't see how?

As for not giving away too much personal information, see above.

As I understand tax avoidancefraud, it happens either by

1. not reporting income in the first place, or
2. by claiming more deductions than took place.

In other words, by illegally reducing the taxable income.

For allowing the public to find tax fraud,

1. cannot be detected by publishing reported income before deductions, and for
2. without knowing what exactly is deduced there is no way to decide whether the deduction was legal or not (which is why you have to detail this to the tax office). Not even the ratio or difference is very informative here. Consider

• a) a web developer employed somewhere around the corner: hardly any deductions but mostly mandatory social insurance and maybe some
• b) a self-employed web developer working from home: hardly any deductions but social insurance which is more variable and higher than in case a)
• c) a farmer, tradesman or shop owner: far higher income (sales), but also far higher deductions buying material/wares and writing off machinery
  As a rule of thumb, IIRC, local shops often have a margin in the lower single-digit percentages of sales.
• d) in my region, part-time farmers are quite common. Or think what happens if the web-designer a) or b) starts a small online shop from home (using the services of a logistic company like amazon: that would not even require a garage for storage).

In the end, even with publishing income before deductions and tax rate, the legal and plausible range will be so wide that I don't see how good conclusions can be drawn.
Moreover, I don't see how any conclusions can be drawn that the tax office couldn't draw far more easily as they have far more information.

Does publishing such information help or hurt?

Coming from a country (Germany) that has had governments for substantial parts (spatially and temporally) of the last century that made extensive and bad use of denounciations, I'm rather wary of the "collateral damage" of such a publication strategy for tax fraud.

Note: Anyone who knows of a tax fraud can already inform the tax office, even anonymously. (This of course may be different in different legislations)

I don't know numbers about tax fraud in this context, but there was an article in the local newspaper a few years ago about anonymous information on animal welfare issues. The interesting points in this context here are that the animal welfare officer explained:

• roughly 1/3 of the reports were actually warranted in the sense that they considered it OK for non-experts to be worried about animal welfare in the respective situation (which doesn't mean that something was actually wrong).
  For example, it's possible to keep sheep and cattle outside on pasture land in winter here. But it may not be easy for a non-farmer/non-vet to decide whether they have suitable conditions for that or not (e.g. whether they need a shed and what exactly is needed).
• another 1/3 of the reports were not warranted in the sense that from the description they could decide there is no problem, but were not able to convince the informer that everything is OK.
  Examples: people worried that ducklings may drown, or thinking that sheep need a heated stable (which is actually bad for them)
• the last 1/3 according to their assessment of the situation were denounciations* out of spite.
  I've actually witnessed a situation that fell into this category, the officer explained that this is quite frequent and that they are of course not allowed to say who informed against the owner of the animal in question. They added that it did not come from the village - and also said that they do see a decided problem with such denunciations* poisoning neighbourhood relations (not knowing who it was creates a whole lot of distrust). Needless to say that even if the animal is kept in perfectly fine conditions this is rather stressful for the holder and involves taking off from work etc.

The officers are required by law to properly make a full case every single time they receive such a report (unless they can convince the worried person that ducklings really won't drown and that sheep do get ill in heated stables and the informer after all decides to withdraw their animal cruelty report).

So for animal welfare, we observe a situation where the officers need to deal with 2 unnecessary cases for every case that actually should be looked into, i.e. the 3fold workload. Plus there's a problem with spiteful denounciations.

Now one difference between the animal health officer and a tax officer is that the tax officer has already far more detailed information available together with far more sophisticated tools to search for suspicious points in the details of the tax declaration. Thus the ratio of reasonable-to-look-into cases to clearly unnecessary cases would probably be far worse than for animal welfare.
As for the spiteful denunciations: just imagine your competitor is tempted to think competition may be much easier if you spend less time on improving your products/serving your customers because you're in the back office serving tax officers due to an extra tax audit...

* denounciation in English seems to be a rather neutral term according to the Wikipedia definition, whereas in German (Denunziation) it is not neutrally reporting someone's (perceived) wrongdoings to the authorities (that would be anzeigen = reporting/informing), but doing so from personal low motives. (I did not find an English translation with this meaning)

Maybe Norwegians are better behaved than Germans in this respect. Or maybe they don't have such anonymous tax fraud reporting possibilities.