How many watts??

Big amps sound beefy, that is what they do. Your loudspeakers may not sound beefy even with big power. You can always borrow a big amp and try it, then you will know. 

Noromance’s comment is so appropriate the name may need to change. 

As has been said by others...
More information is needed, specifically what are the speaker's rated sensitivity. If the sensitivity is low (below 87dB) then you'll need more amp power than speakers with higher sensitivity (above 90dB). Digging deeper, you'll need to know the speakers impedance across the audible frequency range, because speakers have impedance peaks at different frequencies. This is where an amp's current rating comes into play and how well it can provide power through high impedance loads - which in many cases are spontaneous frequency-based loads that will affect sound quality and overall audible response (high-pitch cymbal crash causes a spike in impedance and suddenly the bass is affected because the amp can't provide the power).

In other words, to best answer the question, the make and model of the amp and the speakers is needed to offer the best answer to your question.

Another point is about the description of 1/4 volume and 1/2 volume. This is meaningless because most integrated amps and preamps do not have linear volume control - in other words, 1/2 volume knob adjustment is not necessarily 1/2 volume. I'd completely disregard volume knob fractional increments with respect to actual SPL.

More power is almost always better for sound quality (and loudness) because of the increased head room for instantaneous dynamics. But what matters even more is quality amplification - look for amps that can deliver more power into ever decreasing impedances down to 2 ohms.
Example: The NAD C388 integrated amp is rated:
8 Ohm 250W
4 Ohm 350W
2 Ohm 400W

Please note this example is not high-end by 'audiophile standards' - as a matter of fact it would likely be considered mid-Fi, and is so loaded with features that many are gasping right now that I even mentioned what might be considered a borderline 'lifestyle' product. Its essentially a extremely supped-up Bluesound PowerNode with display, phono stage, dual sub outs, line level outs, MDC card expandability, etc.

Whenever I'm shopping for amps, the first must-have is 2ohm stable; otherwise, its obsolete soon as those demanding (low-impedance) speakers catch your eye.

On jasonbourne comment about running horn speakers with 200 watt amp--is that necessarily a bad thing?  My only experience with Klipsch speakers was at my brother in laws house in another State, and he was using an AVR to drive them that he proudly told me was "500 watts" (probably one of those promos that added all the watts across each channel).  I absolutely hated the sound--every instrument sounded like a saxophone or trombone to my ears--but I always wondered what they might do if driven by one of those 10 watt tube amps. 

Your 80 wpc amp drives your 87db sensitivity speakers rather easily at your preferred volumes; and it has reserves for instantaneous needs. a less powerful amp would be a mistake IMO.

If you like those speakers, I would be tempted to upgrade to their 9.5 speaker

https://www.dagogo.com/salk-sound-ss9-5-speaker-review/
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to answer your question:

it is Logarithmic: a lot of additional power is needed for a small amount of volume increase.

https://geoffthegreygeek.com/amplifier-power/

+3db = a perceptible volume increase. double the WPC needed for +3db volume, i.e. a lot for a little.

to double the volume needs 10x WPC. thus 10x is needed for 2X