Issues with the two option forced choice paradigm and Likert scales

An issue that I have run into a couple of times recently is working with and designing experiments using the two option forced choice paradigm.

I.e The participant is shown a stimuli and asked to press one of two keys. 

Generally the researcher poses a question to the subject that they need to answer about the stimuli in the form of:

"Do you see X?"  If so, press the X key otherwise press the L key.

So, nothing wrong here so far.  The problem I encounter is the subtle issues with the second key.  In the experiments I am thinking about the researcher is thinking about the second key as meaning exactly the inverse of the first key.  For instance.

"Do you see a face in the ink blot?"
Key 1 means "Yes"
Key 2 means "No".

Nothing terrible yet... the semantic issue is tiny at this point.

Now the researcher moves on to the data analysis phase and does some basic stats with their data set. For instance:

Number of times the participant said "Yes" = 50
Number of times the participant said "No" = 50

( face present/ yes button pressed ) =  45
( face not present/yes button pressed ) = 5
( face present/ no button pressed) = 10
( face not present/ no button pressed) 40

These are nice objective summary stats.  No problem.  The problem re-appears when these summary stats are interpreted.

Specifically when the researcher draws a meaningful conclusion that includes the semantics of the "No" button and assumes it actually means "NO I DID NOT SEE THE FACE".  This is WRONG.

Ok, how best to explain this....

This is at its most abstract a signal detection task.   A naive researcher comes to me with some fundamental assumptions about their research and these form the basis for their data analysis and writeup.

Assumption 1 - The stimuli has two cleanly distinct states.
Condition A - Stimuli contains Signal
Condition B - Stimuli does not contain Signal

Assumption 2 - The participant understands the instructions and accurately answers with 100% confidence using the semantics:
Button 1 -> I DO perceive the signal
Button 2 -> I DO NOT perceive the signal

Assumption 3 - Its a perfect world

So... can you spot any of these assumptions that could possibly be weak (or completely bullshit?)

Assumption 1 is usually more realistically stated as
Condition A contains more Signal than condition B and Condition B contains more Noise than Condition A.  (Keeping in mind that there are many other possible signals being perceived at the same time which may be masking, mutating, distracting, modulating or otherwise making a mess of the signal) 
(Also keep in mind that "Noise" must by its very nature have similar properties to the actual signal and the average brain spends lots of time trying to see patterns in noise... so the distinction between noise and signal is usually only a single property)

While its nice when you have a stimuli that contains 100% signal and a stimuli that contains 100% noise... its usually the grey area between the two where things get interesting. 

Ok, So assumption 2.... Otherwise known as "people factors"... is where the slippery slide really starts. 

Assuming the participant actually answers within some reasonable criteria ( not holding down the same key, having a stroke, accidentally responded while texting their girlfriend etc)  then we can tentatively assume that their response has some semantic meaning.  Refer to above for the idealised version from the naive researcher.   The reality is that the semantic meaning of a participant is more often drawn from ( but may be here)

1. Yes I see the signal
2. No I did not see the signal
3. Yes.... I might have seen the signal
4. No.... I might not have seen the signal
5. I don't know if I saw the signal or not
6. Damn.... I got distracted
7. Is this thing on?
8.  Ok, I think this is broken...
9. I need to go to the toilet
10. I'm bored....
11. I wonder what happens if I press both keys at once...
12. When will this bloody experiment end....
13. I hate this experiment....
14. Wish I could get out of here already...
15. Should I wash my hair tonight....
16. I know the researcher asked me to turn my phone off but I didn't and I'm getting a text about my ebay auction....
17. I'm tired.... should have slept last night...
18. I don't want to let that nice researcher down... how can I make them happy?
19.  My eyeballs hurt....
20.  Can I fake an epileptic fit to get out of here....
21. ..... .....  

You get the idea...

The point I'm making is that the using a two option forced choice, means the researcher is asking the participant to map all the above possible answers into two possible semantic cases:

Yes or No.

As you can see this could introduce a great deal of "Noise" in both conditions as the participant needs to do an on-the-fly classification of what they are thinking into two simple categories. 

Is the answer to ask them for a likert scale?   NO!  The solution is to understand that the answers comming from the participant are again a signal stream. 
Ask the participant to answer in clean semantics

Button 1 - Yes I see the signal in the stimuli.
Button 2  - Other. 

This way you get the signal in one class and the noise in the class.  

The key point is that you cannot make assertions about the noise in the writeup.  You have no way to make or verify assumptions about what the participant meant when they hit the "Other" key. (And realistically you should not care) 

The same problem comes when I see research design with a Likert scale with no "Other" column.  This just means that the participant is being forced to push all the noise into the signal data.