Is God swayed by popular appeal?

Question

When we pray for someone to be healed, we pray this individually in the Amidah but we also often have a community misheberach list. I assume that there is a theological reason for the public prayer, and not just to publicize who might need some extra support, especially since you probably have no idea who Plonit bat Sarah is without further context.

Similarly, we often have more than one person praying (individually) for the same person and they know about each other. Do the extra pray-ers help?

What is the benefit to having more than one person pray for the same recipient, either through the public misheberach or through multiple people's private prayers? Surely God, who is just and merciful, would respond to a single prayer in a good cause, and, being all-powerful, does not need to manage a queue where popular requests are dealt with first and multiplied prayer "votes people to the top".

Does God care how many of us pray for a particular person? What is the effect of the multiplied prayer?

This question is prompted by this answer to a question about asking others to pray for someone.

Answer 1

On the verse in Devarim 32:4 הַצּוּר תָּמִים פָּעֳלוֹ, כִּי כָל-דְּרָכָיו מִשְׁפָּט: אֵל אֱמוּנָה וְאֵין עָוֶל, צַדִּיק וְיָשָׁר הוּא, I have heard (do not remember the source) that Hashem is different than a regular ruler. For example - a regular ruler when he punishes a person and puts him in jail for a crime, his wife and children suffer even though they did not commit a crime. However when Hashem punishes a person he takes into account the wife and children, and only if they too are deserving of the loss then will the person die, however if the wife or children are not deserving, then the person will remain alive on account of them.

Based on this, I feel that by a community prayer (Mi Shebeirach) where all those in Shul answer Amen, this adds protection to the sick person as now there are more people affected by this person passing away, and perhaps he will be saved in the merit of one of those that are affected and is not deserving of being affected.