Thanks Lilly* for the thoughtful replies. While I feel like I "get" Contra dancing, I'm not sure I completely "get" Tango, I think replies like yours could help me get it.
Lilly_of_the_valley said:
If you feel absolutely the exact same about everyone else at any given moment (except your DW), I cannot help you here.

...
I'll admit it, it is a bimodal distribution -- there is DW, and then the rest! That's a good first order approximation, but there is some ranking after DW -- some ladies are easier to dance with, and some seem especially appreciative about having been asked (even after the tanda, ha ha).
Lilly_of_the_valley said:
One of my teachers, a great dancer and a true milonguero, used to say: Tango starts in the gaze.
May I suggest an experiment?
Sit out a tanda or two. Watch the floor. Watch women dance. Observe your reactions:
Who catches your attention immediately? In what way?
What makes you stop and watch for a while?
Who do you enjoy to look at more? Why?
Does anyone in particular make you want to approach them, to know them a little better?
This is a good insight on your part. I generally enjoy doing things more than watching them (rather race than watch it, rather ski than watch it, etc.). This has carried over into my Tango, if I'm not dancing I generally go outside or talk to someone, and don't watch the floor much. My "ranking" of who to ask has been based on past experience, or if they are new. I'll have to try your suggested experiment. Maybe if my asking was more intuitive and less algorithmic I wouldn't be asking for algorithms... Who knows, I might even enjoy Tango more. The one way I have done your suggestion a little bit in the past is I feel more like asking something that looks like they are having a good time.
Lilly_of_the_valley said:
To be able to notice and appreciate beauty and attractiveness in others ( including ones of the same, not only the opposite, sex) is not abnormal. Not everyone knows to do that, alas, but it is an ability well worth developing. It is, in its own turn, a very attractive trait! No wonder your wife is popular. She seems to have that genuine positive interest toward most people. And everyone likes to feel attractive, interesting, and liked.
I understand noticing and appreciating beauty -- the human form is one of Mother Nature's crowning works of art. I would get her saying "She is a really good dancer, you should ask her." Instead it is "She is beautiful, ask her." Seems like many men get accused (here on DF, too) of being shallow for using that metric. Put TD in the confused category!
Juniper Ivy said:
It is an important question. You want to maintain harmony in your marriage.
For me I would be happy with the first and last tanda and 2 more tandas in the middle when they play music we both enjoy, for an average evening out lasting 2-3 hours. That would give you plenty of time to dance and talk with other people, while still giving DW the role of being your primary partner. But if DW is sitting out many tandas in frustration due to a lack of dance invites, more attention might be necessary. If she is stuck sitting for 2 or more tandas in a row I would check in with her.
Do you cabaceo DW?
Regarding "sitting for 2 or more tandas in a row:" Yay, a number from a female! I never had cabaceo'd DW, as I would just wait until the tanda started, and if she was unasked I would just walk up to her knowing it would be a "yes"... that is ... until ... recently. A mirada/cabeceo would be a more discreet and gracious way to do this negotiation.
Juniper Ivy said:
I guess the important thing is to be attentive and considerate of both of your feelings and needs - yours and your partner's. And to do what is necessary so you both have a good time. You want to show her she is special and important but still give her the opportunity to interact with other people.
I imagine it can be tricky if you want different things. Like if one person wants to dance more tandas together and the other partner wants to dance more with other people. I can see this would potentially be a sensitive area that could cause hurt feelings and frustration.
That's actually pretty much the whole reason for this thread. If DW was just like TD, we would only dance with each other and the "Not touchy feely" thread would have never been written. She likes to switch partners a lot, while I have been slower to warm up to the idea. Anyway, I think I'm doing pretty well keeping DW happy, and these latest questions have been an attempt to fine tune her happiness to perfection. She and the other ladies have been quite nice about my foibles.