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Is there a mathematical formula for whatever it is that the dominant planet is supposed to be? This is a gimmick not an astrological concept and dominant planet is defined as pretty much whatever the person defining it wants it to be. You will not find this idea under the name "dominant planet" in any authoritative text.
The only thing the skeptics are correct about is that astrology is not an applied science. Astrologers agree with that, too. So anything subjective like "dominant planet" that shows up in a computer program simply reflects the bias of the programmer or the person who hired him to program.
There is a concept called, sometimes, Lord of the Geniture, or chart ruler or almutem (sometimes called almuten) of the chart. Since astrology crosses language barriers it's not unusual to have different names for the same idea or even different ideas with the same name. This would be the most influential planet in the chart, but even this idea isn't what it might seem to the uninitiated. The Lord of the Geniture by definition is the strongest planet in the chart for good. This eliminates the bad actors in search of the good things you wish to do in your life.
The almutem is the strongest planet in a particular place and the alumtem of the ASC is usually chosen as "chart ruler." This is usually, but not always, the same as the domicile or sign ruler. However this planet can be weak or even dangerous. Who wants to be ruled by a debilitated malefic? You can have, in your chart, a debilitated malefic as ASC ruler, but have a very strong Lord of the geniture. You get to choose which one to work with. The ruler of the ASC is sort of a default position. The Lord of the geniture is usually what you want, but have to work for. Lucky you if they are both the same.
Let the computer do the calculating, but you do the thinking. You might have more than one planet that is highly influential. Why ignore it by letting a computer decide which is best? Astrology requires thinking. Don't be like a scientist and let the system think for you.
And this: signs are signs. They do not dominate. Planets act. Signs describe. Libra describes the same thing in every chart only in different areas of life. Astrologers sometimes (and I would add "carelessly") define signs as strong or weak, but as in dominant planet, this is pretty much up to the astrologer as to how to do it. Signs with three or more planets are sometimes described as "strong" or "dominant," but it is the activity of three planets concentrated in a sign that are strong. The sign is just the sign.
Old texts tend to give the signs the lowest priority. Houses first because that is where the action is. Planets next because they are the action. Signs last because they only describe the action. It's true there are "schools" of astrology that have tried chart reading without signs or without houses. They don't work very well.
Back to my main theme. Computers calculate. They don't think for us. Hammers and saws don't build houses. Carpenters build houses using them. The carpenter has to think. Learn to think without a computer. If you're just not interested enough to learn, then ask someone who knows the subject.